The Non-existence of Extremal Objects of Set Theory and the Continuum Problem

Authors

  • Mikhail Valentinovich Antipov Russian Academy of Sciences, Siberian Branch, Novosibirsk, Russia

DOI:

https://doi.org/10.26713/jims.v3i2.48

Keywords:

System of cognition, Infinity axiom, Restriction principle, Insufficiency of basis of fundamental directions, Non-existence and errors of mathematical constructions, Illusion of concepts of infinity, Continuum and cardinalities, First Hilbert problem

Abstract

It is proved that the classical extremal objects of set theory are non-existent. It is also proved that the concepts of uncountability and continuum are erroneous and the first Hilbert problem is incorrect. The infinity axiom and all unlimited objects are unfounded as well.

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CITATION

How to Cite

Antipov, M. V. (2011). The Non-existence of Extremal Objects of Set Theory and the Continuum Problem. Journal of Informatics and Mathematical Sciences, 3(2), 155–176. https://doi.org/10.26713/jims.v3i2.48

Issue

Vol. 3 No. 2 (2011)

Section

Research Articles

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