Set Theory and Logic

    

Invalidating Cantor’s Continuum Hypothesis and Solving Hilbert’s #1 Problem II

Authors: Stephane H. Maes

In this short paper, we provide a mathematical proof that in set theory, developed in a mathematical universe following the ZFC axioms, Cantor’s continuum hypothesis does not hold: the cardinality of the continuous set of all reals is ��, and not א1, i.e., there are infinity א1 (and maybe more than one) between ��, the cardinality of the continuum, and the cardinality of the infinite set of naturals, א0.The proof is derived from combinatorics, relying on ZFC solely for the model of Cantor and Gödel defining א0. It provides input to the still unresolved first of Hilbert famous 23 math problems of interest.This paper, resolves the first of the 23 Hilbert problems with invalidation of the continuum hypothesis.

Comments: 5 Pages.

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Submission history

[v1] 2021-07-22 23:55:37
[v2] 2022-10-25 04:09:50

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