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Open AccessArticle

Solutions of Extension and Limits of Some Cantorian Paradoxes

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Department of Applied Mathematics, University of Alicante, 03690 Alicante, Spain
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Department of Mathematics, University of Alicante, 03690 Alicante, Spain
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Institute of Education, Dublin City University, D09 Y18 Dublin, Ireland
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Author to whom correspondence should be addressed.
Mathematics 2020, 8(4), 486; https://doi.org/10.3390/math8040486
Received: 6 February 2020 / Revised: 16 March 2020 / Accepted: 18 March 2020 / Published: 1 April 2020
Cantor thought of the principles of set theory or intuitive principles as universal forms that can apply to any actual or possible totality. This is something, however, which need not be accepted if there are totalities which have a fundamental ontological value and do not conform to these principles. The difficulties involved are not related to ontological problems but with certain peculiar sets, including the set of all sets that are not members of themselves, the set of all sets, and the ordinal of all ordinals. These problematic totalities for intuitive theory can be treated satisfactorily with the Zermelo and Fraenkel (ZF) axioms or the von Neumann, Bernays, and Gödel (NBG) axioms, and the iterative conceptions expressed in them. View Full-Text
Keywords: cantorian paradoxes; classes; inconsistent totalities; sets; solutions of extension; solutions of limitation cantorian paradoxes; classes; inconsistent totalities; sets; solutions of extension; solutions of limitation
MDPI and ACS Style

Nescolarde-Selva, J.-A.; Usó-Doménech, J.-L.; Segura-Abad, L.; Alonso-Stenberg, K.; Gash, H. Solutions of Extension and Limits of Some Cantorian Paradoxes. Mathematics 2020, 8, 486.

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