Solutions of Extension and Limits of Some Cantorian Paradoxes
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Title: | Solutions of Extension and Limits of Some Cantorian Paradoxes |
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Authors: | Nescolarde-Selva, Josué Antonio | Usó i Domènech, Josep Lluís | Segura, Lorena | Alonso-Stenberg, Kristian | Gash, Hugh |
Research Group/s: | Sistémica, Cibernética y Optimización (SCO) |
Center, Department or Service: | Universidad de Alicante. Departamento de Matemática Aplicada |
Keywords: | Cantorian paradoxes | Classes | Inconsistent totalities | Sets | Solutions of extension | Solutions of limitation |
Knowledge Area: | Matemática Aplicada |
Issue Date: | 1-Apr-2020 |
Publisher: | MDPI |
Citation: | 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(4):486. doi:10.3390/math8040486 |
Abstract: | 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. |
URI: | http://hdl.handle.net/10045/104912 |
ISSN: | 2227-7390 |
DOI: | 10.3390/math8040486 |
Language: | eng |
Type: | info:eu-repo/semantics/article |
Rights: | © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). |
Peer Review: | si |
Publisher version: | https://doi.org/10.3390/math8040486 |
Appears in Collections: | INV - SYC - Artículos de Revistas |
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