Solutions of Extension and Limits of Some Cantorian Paradoxes

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 principle...

Full description

Bibliographic Details
Main Authors:	Josué-Antonio Nescolarde-Selva, José-Luis Usó-Doménech, Lorena Segura-Abad, Kristian Alonso-Stenberg, Hugh Gash
Format:	Article
Language:	English
Published:	MDPI AG 2020-04-01
Series:	Mathematics
Subjects:	cantorian paradoxes classes inconsistent totalities sets solutions of extension solutions of limitation
Online Access:	https://www.mdpi.com/2227-7390/8/4/486

id	doaj-0bb76ea1a1224f36a238be45d63d0807
record_format	Article
spelling	doaj-0bb76ea1a1224f36a238be45d63d08072020-11-25T02:37:26ZengMDPI AGMathematics2227-73902020-04-01848648610.3390/math8040486Solutions of Extension and Limits of Some Cantorian ParadoxesJosué-Antonio Nescolarde-Selva0José-Luis Usó-Doménech1Lorena Segura-Abad2Kristian Alonso-Stenberg3Hugh Gash4Department of Applied Mathematics, University of Alicante, 03690 Alicante, SpainDepartment of Applied Mathematics, University of Alicante, 03690 Alicante, SpainDepartment of Mathematics, University of Alicante, 03690 Alicante, SpainDepartment of Applied Mathematics, University of Alicante, 03690 Alicante, SpainInstitute of Education, Dublin City University, D09 Y18 Dublin, IrelandCantor 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.https://www.mdpi.com/2227-7390/8/4/486cantorian paradoxesclassesinconsistent totalitiessetssolutions of extensionsolutions of limitation
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Josué-Antonio Nescolarde-Selva José-Luis Usó-Doménech Lorena Segura-Abad Kristian Alonso-Stenberg Hugh Gash
spellingShingle	Josué-Antonio Nescolarde-Selva José-Luis Usó-Doménech Lorena Segura-Abad Kristian Alonso-Stenberg Hugh Gash Solutions of Extension and Limits of Some Cantorian Paradoxes Mathematics cantorian paradoxes classes inconsistent totalities sets solutions of extension solutions of limitation
author_facet	Josué-Antonio Nescolarde-Selva José-Luis Usó-Doménech Lorena Segura-Abad Kristian Alonso-Stenberg Hugh Gash
author_sort	Josué-Antonio Nescolarde-Selva
title	Solutions of Extension and Limits of Some Cantorian Paradoxes
title_short	Solutions of Extension and Limits of Some Cantorian Paradoxes
title_full	Solutions of Extension and Limits of Some Cantorian Paradoxes
title_fullStr	Solutions of Extension and Limits of Some Cantorian Paradoxes
title_full_unstemmed	Solutions of Extension and Limits of Some Cantorian Paradoxes
title_sort	solutions of extension and limits of some cantorian paradoxes
publisher	MDPI AG
series	Mathematics
issn	2227-7390
publishDate	2020-04-01
description	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.
topic	cantorian paradoxes classes inconsistent totalities sets solutions of extension solutions of limitation
url	https://www.mdpi.com/2227-7390/8/4/486
work_keys_str_mv	AT josueantonionescolardeselva solutionsofextensionandlimitsofsomecantorianparadoxes AT joseluisusodomenech solutionsofextensionandlimitsofsomecantorianparadoxes AT lorenaseguraabad solutionsofextensionandlimitsofsomecantorianparadoxes AT kristianalonsostenberg solutionsofextensionandlimitsofsomecantorianparadoxes AT hughgash solutionsofextensionandlimitsofsomecantorianparadoxes
_version_	1724795650725380096

Solutions of Extension and Limits of Some Cantorian Paradoxes

Similar Items