Set Theory and Logic

    

Cardinal Numbers and Cantor’s Continuum Hypothesis

Authors: Jincheng Zhang

:In this paper, the cardinal number problem is discussed separately in the axiom systems for set theory SZF+ and SZF-. It can be proved that:ordinal numbers and cardinal numbers are unified. There is no uncountable cardinal number; in Cantor’s set theory, definitions, theorems and propositions based on uncountable cardinal numbers and ordinal numbers are all false. In fact, Cantor’s continuum hypothesis is the cardinal number of a set of natural numbers, and whether there are other cardinal numbers between cardinal numbers of set of natural numbers |N| and cardinal numbers of power set |P (N)|, different interpretations are given in different axiom systems.

Comments: 10 Pages.

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Submission history

[v1] 2023-05-06 00:43:19

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