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28 pages, 2865 KB  
Article
Probabilistic Assessment of Solar-Based Hydrogen Production Using PVGIS, Metalog Distributions, and LCOH Modeling
by Jacek Caban, Arkadiusz Małek and Zbigniew Siemiątkowski
Energies 2025, 18(18), 4972; https://doi.org/10.3390/en18184972 - 18 Sep 2025
Viewed by 3024
Abstract
The transition toward low-carbon energy systems requires reliable tools for assessing renewable-based hydrogen production under real-world climatic and economic conditions. This study presents a novel probabilistic framework integrating the following three complementary elements: (1) a Photovoltaic Geographical Information System (PVGIS) for high-resolution, location-specific [...] Read more.
The transition toward low-carbon energy systems requires reliable tools for assessing renewable-based hydrogen production under real-world climatic and economic conditions. This study presents a novel probabilistic framework integrating the following three complementary elements: (1) a Photovoltaic Geographical Information System (PVGIS) for high-resolution, location-specific solar energy data; (2) Metalog probability distributions for advanced modeling of variability and uncertainty in photovoltaic (PV) energy generation; and (3) Levelized Cost of Hydrogen (LCOH) calculations to evaluate the economic viability of hydrogen production systems. The methodology is applied to three diverse European locations—Lublin (Poland), Budapest (Hungary), and Malaga (Spain)—to demonstrate regional differences in hydrogen production potential. The results indicate annual PV energy yields of 108.3 MWh, 124.6 MWh, and 170.95 MWh, respectively, which translate into LCOH values of EUR 9.67/kg (Poland), EUR 8.40/kg (Hungary), and EUR 6.13/kg (Spain). The probabilistic analysis reveals seasonal production risks and quantifies the probability of achieving specific monthly energy thresholds, providing critical insights for designing systems with continuous hydrogen output. This combined use of a PVGIS, Metalog, and LCOH calculations offers a unique decision-support tool for investors, policymakers, and SMEs planning green hydrogen projects. The proposed methodology is scalable and adaptable to other renewable energy systems, enabling informed investment decisions and improved regional energy transition strategies. Full article
(This article belongs to the Section A5: Hydrogen Energy)
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21 pages, 892 KB  
Article
A Meta-Logical Framework for the Equivalence of Syntactic and Semantic Theories
by Maria Dimarogkona, Petros Stefaneas and Nicola Angius
Philosophies 2025, 10(4), 78; https://doi.org/10.3390/philosophies10040078 - 27 Jun 2025
Viewed by 1166
Abstract
This paper introduces a meta-logical framework—based on the theory of institutions (a categorical version of abstract model theory)—to be used as a tool for the formalization of the two main views regarding the structure of scientific theories, namely the syntactic and the semantic [...] Read more.
This paper introduces a meta-logical framework—based on the theory of institutions (a categorical version of abstract model theory)—to be used as a tool for the formalization of the two main views regarding the structure of scientific theories, namely the syntactic and the semantic views, as they have emerged from the relevant contemporary discussion. The formalization leads to a proof of the equivalence of the two views, which supports the claim that the two approaches are not really in tension. The proof is based on the Galois connection between classes of sentences and classes of models defined over some institution. First, the history of the syntactic–semantic debate is recalled and the theory of institutions formally introduced. Secondly, the notions of syntactic and semantic theories are formalized within the institution and their equivalence proved. Finally, the novelty of the proposed framework is highlighted with respect to existing formalizations. Full article
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15 pages, 1088 KB  
Article
A Novel Evaluation of Income Class Boundaries Using Inflection Points of Probability Density Functions: A Case Study of Brazil
by Rafael Bittencourt, Hernane Borges de Barros Pereira, Marcelo A. Moret, Ivan C. Da Cunha Lima and Serge Galam
Entropy 2025, 27(2), 186; https://doi.org/10.3390/e27020186 - 12 Feb 2025
Viewed by 3083
Abstract
Categorizing a population into different income classes is important for creating effective policies and analyzing markets. Our study develops a statistical method based on a nationwide survey of income distribution. We use these data to create a cumulative distribution function with a metalogistic [...] Read more.
Categorizing a population into different income classes is important for creating effective policies and analyzing markets. Our study develops a statistical method based on a nationwide survey of income distribution. We use these data to create a cumulative distribution function with a metalogistic distribution and its probability density function. We propose a new way to divide the population into income classes by using the inflection points of the probability density function as the class boundaries. As a case study, we apply this method to income data from Brazil between 2012 and 2022. We identify five income classes, with both their boundaries and the distribution of the population changing over time. To check our approach, we calculate the Gini coefficient and find that our results closely match official figures, with a root mean square deviation of less than 1%. By using individual income instead of family income, we avoid distortions caused by the fact that poorer families tend to be larger than wealthier ones. In the end, we identify five main income classes, with their boundaries shifting each year, reflecting the changing nature of income distribution in society. Full article
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23 pages, 5065 KB  
Article
Probabilistic Analysis of Low-Emission Hydrogen Production from a Photovoltaic Carport
by Arkadiusz Małek, Agnieszka Dudziak, Jacek Caban and Jonas Matijošius
Appl. Sci. 2024, 14(20), 9531; https://doi.org/10.3390/app14209531 - 18 Oct 2024
Cited by 8 | Viewed by 1512
Abstract
This article presents a 3D model of a yellow hydrogen generation system that uses the electricity produced by a photovoltaic carport. The 3D models of all key system components were collected, and their characteristics were described. Based on the design of the 3D [...] Read more.
This article presents a 3D model of a yellow hydrogen generation system that uses the electricity produced by a photovoltaic carport. The 3D models of all key system components were collected, and their characteristics were described. Based on the design of the 3D model of the photovoltaic carport, the amount of energy produced monthly was determined. These quantities were then applied to determine the production of low-emission hydrogen. In order to increase the amount of low-emission hydrogen produced, the usage of a stationary energy storage facility was proposed. The Metalog family of probability distributions was adopted to develop a strategic model for low-emission hydrogen production. The hydrogen economy of a company that uses small amounts of hydrogen can be based on such a model. The 3D modeling and calculations show that it is possible to design a compact low-emission hydrogen generation system using rapid prototyping tools, including the photovoltaic carport with an electrolyzer placed in the container and an energy storage facility. This is an effective solution for the climate and energy transition of companies with low hydrogen demand. In the analytical part, the Metalog probability distribution family was employed to determine the amount of monthly energy produced by 6.3 kWp photovoltaic systems located in two European countries: Poland and Italy. Calculating the probability of producing specific amounts of hydrogen in two European countries is an answer to a frequently asked question: In which European countries will the production of low-emission hydrogen from photovoltaic systems be the most profitable? As a result of the calculations, for the analyzed year 2023 in Poland and Italy, specific answers were obtained regarding the probability of monthly energy generation and monthly hydrogen production. Many companies from Poland and Italy are taking part in the European competition to create hydrogen banks. Only those that offer low-emission hydrogen at the lowest prices will receive EU funding. Full article
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22 pages, 4605 KB  
Article
Probabilistic Analysis of Green Hydrogen Production from a Mix of Solar and Wind Energy
by Agnieszka Dudziak, Arkadiusz Małek, Andrzej Marciniak, Jacek Caban and Jarosław Seńko
Energies 2024, 17(17), 4387; https://doi.org/10.3390/en17174387 - 2 Sep 2024
Cited by 4 | Viewed by 2025
Abstract
This article describes an example of using the measurement data from photovoltaic systems and wind turbines to perform practical probabilistic calculations around green hydrogen generation. First, the power generated in one month by a ground-mounted photovoltaic system with a peak power of 3 [...] Read more.
This article describes an example of using the measurement data from photovoltaic systems and wind turbines to perform practical probabilistic calculations around green hydrogen generation. First, the power generated in one month by a ground-mounted photovoltaic system with a peak power of 3 MWp is described. Using the Metalog family of probability distributions, the probability of generating selected power levels corresponding to the amount of green hydrogen produced is calculated. Identical calculations are performed for the simulation data, allowing us to determine the power produced by a wind turbine with a maximum power of 3.45 MW. After interpolating both time series of the power generated by the renewable energy sources to a common sampling time, they are summed. For the sum of the power produced by the photovoltaic system and the wind turbine, the probability of generating selected power levels corresponding to the amount of green hydrogen produced is again calculated. The presented calculations allow us to determine, with probability distribution accuracy, the amount of hydrogen generated from the energy sources constituting a mix of photovoltaics and wind. The green hydrogen production model includes the hardware and the geographic context. It can be used to determine the preliminary assumptions related to the production of large amounts of green hydrogen in selected locations. The calculations presented in this article are a practical example of Business Intelligence. Full article
(This article belongs to the Special Issue Advanced Forecasting Methods for Sustainable Power Grid)
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25 pages, 4840 KB  
Article
Application of the Metalog Probability Distribution Family to Predict Energy Production by Photovoltaic Systems for the Purposes of Generating Green Hydrogen
by Arkadiusz Małek, Jacek Caban, Monika Stoma, Agnieszka Dudziak and Branislav Šarkan
Energies 2024, 17(15), 3729; https://doi.org/10.3390/en17153729 - 29 Jul 2024
Viewed by 1683
Abstract
The article presents the application of the metalog family of probability distributions to predict the energy production of photovoltaic systems for the purpose of generating small amounts of green hydrogen in distributed systems. It can be used for transport purposes as well as [...] Read more.
The article presents the application of the metalog family of probability distributions to predict the energy production of photovoltaic systems for the purpose of generating small amounts of green hydrogen in distributed systems. It can be used for transport purposes as well as to generate energy and heat for housing purposes. The monthly and daily amounts of energy produced by a photovoltaic system with a peak power of 6.15 kWp were analyzed using traditional statistical methods and the metalog probability distribution family. On this basis, it is possible to calculate daily and monthly amounts of hydrogen produced with accuracy from the probability distribution. Probabilistic analysis of the instantaneous power generated by the photovoltaic system was used to determine the nominal power of the hydrogen electrolyzer. In order to use all the energy produced by the photovoltaic system to produce green hydrogen, the use of a stationary energy storage device was proposed and its energy capacity was determined. The calculations contained in the article can be used to design home green hydrogen production systems and support the climate and energy transformation of small companies with a hydrogen demand of up to ¾ kg/day. Full article
(This article belongs to the Special Issue Sustainable Development of Fuel Cells and Hydrogen Technologies)
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21 pages, 7618 KB  
Article
A Method for Assessing the Technical Condition of Traction Batteries Using the Metalog Family of Probability Distributions
by Jacek Caban, Arkadiusz Małek and Dariusz Kroczyński
Energies 2024, 17(13), 3096; https://doi.org/10.3390/en17133096 - 23 Jun 2024
Cited by 8 | Viewed by 2076
Abstract
The aim of the research presented in the article is to use the Metalog family of probability distributions to assess the technical condition of traction battery packs from electric and hybrid vehicles. The description of the research object, which is a battery pack [...] Read more.
The aim of the research presented in the article is to use the Metalog family of probability distributions to assess the technical condition of traction battery packs from electric and hybrid vehicles. The description of the research object, which is a battery pack from a hybrid vehicle, will be provided. Then, a system for controlled charging and discharging of individual cells in a battery pack will be reviewed. It is an essential diagnostic and research device used to determine the capacity of individual cells. The capacity values of all battery cells will then be analyzed using the Metalog probability distribution family. The use of this tool allows us to determine the Probability Density Function for the entire battery pack. Based on this, the diagnostician is able to assess the technical condition of the tested package and decide on its further fate. It can be intended for repair, employed as a stationary energy storage facility, or used for disposal. The algorithm for assessing the technical condition of traction batteries proposed by the authors can be used in all battery packs regardless of the type of cells used and their energy capacity. Full article
(This article belongs to the Special Issue Advances in Fuel Cells and Hydrogen Storage Technologies)
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24 pages, 2196 KB  
Article
Strategic Model for Yellow Hydrogen Production Using the Metalog Family of Probability Distributions
by Arkadiusz Małek, Agnieszka Dudziak, Jacek Caban and Monika Stoma
Energies 2024, 17(10), 2398; https://doi.org/10.3390/en17102398 - 16 May 2024
Cited by 11 | Viewed by 2184
Abstract
Storing energy in hydrogen has been recognized by scientists as one of the most effective ways of storing energy for many reasons. The first of these reasons is the availability of technology for producing hydrogen from water using electrolytic methods. Another aspect is [...] Read more.
Storing energy in hydrogen has been recognized by scientists as one of the most effective ways of storing energy for many reasons. The first of these reasons is the availability of technology for producing hydrogen from water using electrolytic methods. Another aspect is the availability of relatively cheap energy from renewable energy sources. Moreover, you can count on the availability of large amounts of this energy. The aim of this article is to support the decision-making processes related to the production of yellow hydrogen using a strategic model which exploits the metalog family of probability distributions. This model allows us to calculate, with accuracy regarding the probability distribution, the amount of energy produced by photovoltaic systems with a specific peak power. Using the model in question, it is possible to calculate the expected amount of electricity produced daily from the photovoltaic system and the corresponding amount of yellow hydrogen produced. Such a strategic model may be appropriate for renewable energy developers who build photovoltaic systems intended specifically for the production of yellow and green hydrogen. Based on our model, they can estimate the size of the photovoltaic system needed to produce the assumed hydrogen volume. The strategic model can also be adopted by producers of green and yellow hydrogen. Due to precise calculations, up to the probability distribution, the model allows us to calculate the probability of providing the required energy from a specific part of the energy mix. Full article
(This article belongs to the Special Issue Advances in Hydrogen Energy III)
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17 pages, 1020 KB  
Article
The Basics of Home Office (Re)institutionalisation from the Perspective of Experiences from the COVID-19 Era
by Janusz Rymaniak, Vida Davidavičienė and Katarzyna Lis
Sustainability 2024, 16(9), 3606; https://doi.org/10.3390/su16093606 - 25 Apr 2024
Cited by 2 | Viewed by 1975
Abstract
After COVID-19, the dynamics of home office development slowed down. According to the experiences of major companies, the problem is “fluctuating”. Research from the pandemic era covers various aspects and fails to present the concept of synthetic developmental conditions. Therefore, the issue of [...] Read more.
After COVID-19, the dynamics of home office development slowed down. According to the experiences of major companies, the problem is “fluctuating”. Research from the pandemic era covers various aspects and fails to present the concept of synthetic developmental conditions. Therefore, the issue of extending the organisation to home spaces was undertaken, identifying the determinants of the sustainable development of workplaces and organisations. The key is to create sustainable work systems, i.e., adapted to the environment, while being creative, critical, and productive. This study aims to establish the cultural determinants of home office development based on empirical research from the perspective of neo-institutionalism. For this purpose, the institutional logics were subject to operationalisation and the co-dependencies of metalogics with the types of organisational cultures assumed in the Cameron–Quinn OCAI model were established. The information was collected in a CAWI survey. The presented research procedure constitutes a methodical innovation. The results demonstrate a trend of changes in the dominating types of organisational culture from market control to cooperation and creation with a stimulating role of professional logics (occupation, organisation) from the perspective of working from home which brings sustainable management and business models. There is a subtle role of home logic and low employee readiness level. The adapted cultural approach demonstrates that increasing effectiveness of home office solutions requires development of integrated practices, which consider this type of work as separate and specialised. The past corporate failures and spontaneous methods cannot serve as grounds for strategies (long-term solutions). However, the research demonstrates a low level and limited range of employee impact on the organisational culture. It also indicates the need for additional analyses to determine the concept of designing workplaces in the Sustainability–Harmonisation trajectory. Full article
(This article belongs to the Special Issue Technology-Driven Entrepreneurship for a Sustainable Future)
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17 pages, 3053 KB  
Article
Strategic Model for Charging a Fleet of Electric Vehicles with Energy from Renewable Energy Sources
by Jacek Caban, Arkadiusz Małek and Branislav Šarkan
Energies 2024, 17(5), 1264; https://doi.org/10.3390/en17051264 - 6 Mar 2024
Cited by 15 | Viewed by 2821
Abstract
The ever-growing number of electric vehicles requires increasing amounts of energy to charge their traction batteries. Electric vehicles are the most ecological when the energy for charging them comes from renewable energy sources. Obtaining electricity from renewable sources such as photovoltaic systems is [...] Read more.
The ever-growing number of electric vehicles requires increasing amounts of energy to charge their traction batteries. Electric vehicles are the most ecological when the energy for charging them comes from renewable energy sources. Obtaining electricity from renewable sources such as photovoltaic systems is also a way to reduce the operating costs of an electric vehicle. However, to produce cheap electricity from renewable energy sources, you first need to invest in the construction of a photovoltaic system. The article presents a strategic model for charging a fleet of electric vehicles with energy from photovoltaic systems. The model is useful for sizing a planned photovoltaic system to the energy needs of a vehicle fleet. It uses the Metalog family of probability distributions to determine the probability of producing a given amount of energy needed to power electric vehicle chargers. Using the model, it is possible to determine the percentage of energy from photovoltaic systems in the total energy needed to charge a vehicle fleet. The research was carried out on real data from an operating photovoltaic system with a peak power of 50 kWp. The approach presented in the strategic model takes into account the geographical and climatic context related to the location of the photovoltaic system. The model can be used for various renewable energy sources and different sizes of vehicle fleets with different electricity demands to charge their batteries. The presented model can be used to manage the energy produced both at the design stage of the photovoltaic system and during its operation. Full article
(This article belongs to the Special Issue Electricity Market Modeling Trends in Power Systems)
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16 pages, 6585 KB  
Article
A Method of Assessing the Selection of Carport Power for an Electric Vehicle Using the Metalog Probability Distribution Family
by Arkadiusz Małek, Jacek Caban, Agnieszka Dudziak, Andrzej Marciniak and Piotr Ignaciuk
Energies 2023, 16(13), 5077; https://doi.org/10.3390/en16135077 - 30 Jun 2023
Cited by 13 | Viewed by 1927
Abstract
This article presents a method for assessing the selection of carport power for an electric vehicle using the Metalog probability distribution family. Carports are used to generate electricity and provide shade for vehicles parked underneath them. On the roof of the carport, there [...] Read more.
This article presents a method for assessing the selection of carport power for an electric vehicle using the Metalog probability distribution family. Carports are used to generate electricity and provide shade for vehicles parked underneath them. On the roof of the carport, there is a photovoltaic system consisting of photovoltaic panels and an inverter. An inverter with Internet of Things functions generates data packets which describe the operation of the entire system at certain intervals and sends them via wireless transmission to a cloud server. The transmitted data can be processed offline and used to determine the charging capacity of individual electric vehicles. This article presents the use of the Metalog family of distributions to predict the production of electricity by a photovoltaic carport with the accuracy of the probability distribution. Based on the calculations, an electric vehicle was selected that can be charged from the carport. Full article
(This article belongs to the Special Issue Advances in Photovoltaic Solar Energy)
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16 pages, 3265 KB  
Article
Selection of a Photovoltaic Carport Power for an Electric Vehicle
by Edgar Sokolovskij, Arkadiusz Małek, Jacek Caban, Agnieszka Dudziak, Jonas Matijošius and Andrzej Marciniak
Energies 2023, 16(7), 3126; https://doi.org/10.3390/en16073126 - 29 Mar 2023
Cited by 15 | Viewed by 3074
Abstract
The increasing number of electric vehicles is forcing new solutions in the field of charging infrastructure. One such solution is photovoltaic carports, which have a double task. Firstly, they enable the generation of electricity to charge vehicles, and secondly, they protect the vehicle [...] Read more.
The increasing number of electric vehicles is forcing new solutions in the field of charging infrastructure. One such solution is photovoltaic carports, which have a double task. Firstly, they enable the generation of electricity to charge vehicles, and secondly, they protect the vehicle against the excessive heating of its interior. This article presents the functioning of a small carport for charging an electric vehicle. Attention is drawn to the problems of selecting the peak power of the photovoltaic system for charging an electric vehicle. An economic and energy analysis is carried out for the effective use of photovoltaic carports. In this article, we present the use of the Metalog family of distributions to predict the production of electricity by a photovoltaic carport with the accuracy of probability distribution. Full article
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14 pages, 1879 KB  
Article
Extreme Path Delay Estimation of Critical Paths in Within-Die Process Fluctuations Using Multi-Parameter Distributions
by Miikka Runolinna, Matthew Turnquist, Jukka Teittinen, Pauliina Ilmonen and Lauri Koskinen
J. Low Power Electron. Appl. 2023, 13(1), 22; https://doi.org/10.3390/jlpea13010022 - 20 Mar 2023
Cited by 4 | Viewed by 2807
Abstract
Two multi-parameter distributions, namely the Pearson type IV and metalog distributions, are discussed and suggested as alternatives to the normal distribution for modelling path delay data that determines the maximum clock frequency (FMAX) of a microprocessor or other digital circuit. These distributions outperform [...] Read more.
Two multi-parameter distributions, namely the Pearson type IV and metalog distributions, are discussed and suggested as alternatives to the normal distribution for modelling path delay data that determines the maximum clock frequency (FMAX) of a microprocessor or other digital circuit. These distributions outperform the normal distribution in goodness-of-fit statistics for simulated path delay data derived from a fabricated microcontroller, with the six-term metalog distribution offering the best fit. Furthermore, 99.7% confidence intervals are calculated for some extreme quantiles on each dataset using the previous distributions. Considering the six-term metalog distribution estimates as the golden standard, the relative errors in single paths vary between 4 and 14% for the normal distribution. Finally, the within-die (WID) variation maximum critical path delay distribution for multiple critical paths is derived under the assumption of independence between the paths. Its density function is then used to compute different maximum delays for varying numbers of critical paths, assuming each path has one of the previous distributions with the metalog estimates as the golden standard. For 100 paths, the relative errors are at most 14% for the normal distribution. With 1000 and 10,000 paths, the corresponding errors extend up to 16 and 19%, respectively. Full article
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20 pages, 744 KB  
Article
What’s Love Got to Do with It? Religion and the Multiple Logic Tensions of Social Enterprise
by Bruce R. Borquist
Religions 2021, 12(8), 655; https://doi.org/10.3390/rel12080655 - 18 Aug 2021
Cited by 9 | Viewed by 4737
Abstract
This paper develops a model that advances our understanding of how social enterprises respond to the complexity of a constellation of multiple, often competing goals, referred to here as institutional logics. Introducing a religious logic to the recognised social welfare and commercial logics [...] Read more.
This paper develops a model that advances our understanding of how social enterprises respond to the complexity of a constellation of multiple, often competing goals, referred to here as institutional logics. Introducing a religious logic to the recognised social welfare and commercial logics of social enterprise, this model builds on a religious worldview foundation and incorporates religion-inspired altruistic love and non-transactional giving as its scaffolding. A comparative case study of faith-based, faith-inspired and secular organisations located in Southeast Asia demonstrates the origin and applicability of the model. Findings highlight that religion serves as an overarching logic, or “metalogic”, and frame of reference. Faith-based social enterprises use this religious logic to redefine perceived paradoxical tensions between the social welfare and commercial objectives they embody. Study results advance knowledge on organisational responses to multiple logic prescriptions, underscores the influence of religion, altruistic love and giving on organisational behaviour and contributes to the scarce literature on faith-based social enterprises. Full article
(This article belongs to the Special Issue Social Entrepreneurship from a Christian Perspective)
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14 pages, 673 KB  
Article
On Certain Axiomatizations of Arithmetic of Natural and Integer Numbers
by Urszula Wybraniec-Skardowska
Axioms 2019, 8(3), 103; https://doi.org/10.3390/axioms8030103 - 4 Sep 2019
Cited by 5 | Viewed by 3913
Abstract
The systems of arithmetic discussed in this work are non-elementary theories. In this paper, natural numbers are characterized axiomatically in two different ways. We begin by recalling the classical set P of axioms of Peano’s arithmetic of natural numbers proposed in 1889 (including [...] Read more.
The systems of arithmetic discussed in this work are non-elementary theories. In this paper, natural numbers are characterized axiomatically in two different ways. We begin by recalling the classical set P of axioms of Peano’s arithmetic of natural numbers proposed in 1889 (including such primitive notions as: set of natural numbers, zero, successor of natural number) and compare it with the set W of axioms of this arithmetic (including the primitive notions like: set of natural numbers and relation of inequality) proposed by Witold Wilkosz, a Polish logician, philosopher and mathematician, in 1932. The axioms W are those of ordered sets without largest element, in which every non-empty set has a least element, and every set bounded from above has a greatest element. We show that P and W are equivalent and also that the systems of arithmetic based on W or on P, are categorical and consistent. There follows a set of intuitive axioms PI of integers arithmetic, modelled on P and proposed by B. Iwanuś, as well as a set of axioms WI of this arithmetic, modelled on the W axioms, PI and WI being also equivalent, categorical and consistent. We also discuss the problem of independence of sets of axioms, which were dealt with earlier. Full article
(This article belongs to the Special Issue Deductive Systems in Traditional and Modern Logic)
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