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

Mikhail Valentinovich Antipov

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.

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

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DOI: http://dx.doi.org/10.26713%2Fjims.v3i2.48

eISSN 0975-5748; pISSN 0974-875X