Set Theory and Logic

    

Any Formal System That Contains Sets Arithmetic and Rational Numbers is Inconsistent

Authors: Jim Rock

Gӧdel proved that any formal system containing arithmetic is incomplete. We show that any such formal system is inconsistent. We establish a collection of nested sets of rational numbers in a descending hierarchy. The sets higher in the descending hierarchy contain element(s) that are not in the sets below them in the hierarchy. Given such a descending set hierarchy, it is easy to develop two arguments that contradict each other. The conclusion of Argument#2 is false. But, Argument#2 is a valid argument.

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[v1] 2023-07-07 21:36:24
[v2] 2023-09-25 22:55:19

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