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Mathematical Logic and Foundations of Mathematics
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Mathematical Logic and Foundations of Mathematics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: 30 November 2025 | Viewed by 1759

Special Issue Editors

Dr. Andrei Alexandru

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Guest Editor
Institute of Computer Science, Romanian Academy, 700505 Iaşi, Romania
Interests: mathematical logic; set theory; algebra
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Gabriel Ciobanu

E-Mail Website
Guest Editor
Institute of Computer Science, IIT, Romanian Academy (Iasi branch), A.I. Cuza University, 700481 Iasi, Romania
Interests: formal models and methods in computer science; process calculi; permutation models in set theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Mathematical logic is often divided into fields of set theory, model theory, recursion theory, and proof theory. This Special Issue will consider high-quality papers which present original research in mathematical logic and the foundations of mathematics. There will be a particular emphasis on set theory and the several axiomatic systems that have been proposed over time in accordance with our intuition (avoiding paradoxes). We hope to produce desirable results, presenting enough papers with credible rationales and stimulating approaches for understanding the fundamental constructions of mathematics and set theory.

We expect papers covering the following topics: model theory, recursion theory, proof theory, set theory, or algebraic logic. Articles challenging the traditional axiomatization, which includes the axiom of choice, the choice principles (that are weaker versions of the axiom of choice), the axiom of foundation, and the axiom of infinity, are very welcome, as well as those related to set theories with atoms and finitely supported structures. We will accept manuscripts specifically focusing on applications of set theory and logic to (theoretical) computer science (semantics,  domain theory, rewriting systems, reversibility).  

Dr. Andrei Alexandru
Prof. Dr. Gabriel Ciobanu
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • set theory
  • alternative axioms
  • consistency
  • primitive recursive arithmetic
  • set with atoms
  • axiom of choice
  • finitely supported sets
  • logic in computer science
  • applications of logic

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Published Papers (2 papers)

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Research

15 pages, 355 KiB  
Article
On the Uniform Projection and Covering Problems in Descriptive Set Theory Under the Axiom of Constructibility
by Vladimir Kanovei and Vassily Lyubetsky
Mathematics 2025, 13(3), 409; https://doi.org/10.3390/math13030409 - 26 Jan 2025
Viewed by 478
Abstract
The following two consequences of the axiom of constructibility V=L will be established for every n≥3: 1. Every linear Σn1 set is the projection of a uniform planar Πn−11 set. 2. There [...] Read more.
The following two consequences of the axiom of constructibility V=L will be established for every n≥3: 1. Every linear Σn1 set is the projection of a uniform planar Πn−11 set. 2. There is a planar Πn−11 set with countable cross-sections not covered by a union of countably many uniform Σn1 sets. If n=2 then claims 1 and 2 hold in ZFC alone, without the assumption of V=L. Full article
(This article belongs to the Special Issue Mathematical Logic and Foundations of Mathematics)
23 pages, 318 KiB  
Article
Computably Enumerable Semisimple Rings
by Huishan Wu
Mathematics 2025, 13(3), 337; https://doi.org/10.3390/math13030337 - 21 Jan 2025
Viewed by 639
Abstract
The theory of semisimple rings plays a fundamental role in noncommutative algebra. We study the complexity of the problem of semisimple rings using the tools of computability theory. Following the general idea of computably enumerable (c.e. for short) universal algebras, we define a [...] Read more.
The theory of semisimple rings plays a fundamental role in noncommutative algebra. We study the complexity of the problem of semisimple rings using the tools of computability theory. Following the general idea of computably enumerable (c.e. for short) universal algebras, we define a c.e. ring as the quotient ring of a computable ring modulo a c.e. congruence relation and view such rings as structures in the language of rings, together with a binary relation. We formalize the problem of being semisimple for a c.e. ring by the corresponding index set and prove that the index set of c.e. semisimple rings is Σ30-complete. This reveals that the complexity of the definability of c.e. semisimple rings lies exactly in the Σ30 of the arithmetic hierarchy. As applications of the complexity results on semisimple rings, we also obtain the optimal complexity results on other closely connected classes of rings, such as the small class of finite direct products of fields and the more general class of semiperfect rings. Full article
(This article belongs to the Special Issue Mathematical Logic and Foundations of Mathematics)
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