Set Theory and Logic


Two Results on ZFC: (1) if ZFC is Consistent Then it is Deductively Incomplete, (2) ZFC is Inconsistent

Authors: Thomas Colignatus

The Zermelo-Fraenkel-Axiom-of-Choice (ZFC) system of axioms for set theory appears to be inconsistent. A step in developing this proof is the observation that ZFC would be deductively incomplete if it were consistent. Both points are proven by means of the singleton. The axioms are still too lax on the notion of a well-defined set.

Comments: 13 Pages.

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Submission history

[v1] 2015-06-19 08:23:22
[v2] 2015-06-24 10:54:12
[v3] 2015-06-27 03:05:22
[v4] 2015-07-26 23:12:31

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