## ZFC is Inconsistent. A Condition by Paul of Venice (1369-1429) Solves Russell's Paradox, Blocks Cantor's Diagonal Argument, and Provides a Challenge to ZFC

**Authors:** Thomas Colignatus

Paul of Venice (1369-1429) provides a consistency condition that resolves Russell's Paradox in naive set theory without using a theory of types. It allows a set of all sets. It also blocks the (diagonal) general proof of Cantor's Theorem (in Russell's form, for the power set). The Zermelo-Fraenkel-Axiom-of-Choice (ZFC) axioms for set theory appear to be inconsistent. They are still too lax on the notion of a well-defined set. The transfinites of ZFC may be a mirage, and a consequence of still imperfect axiomatics in ZFC for the foundations of set theory. For amendment of ZFC two alternatives are mentioned: ZFC-PV (amendment of de Axiom of Separation) or BST (Basic Set Theory).

**Comments:** 2 Pages. The paper refers to the book FMNAI that supersedes the paper

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### Submission history

[v1] 2014-12-25 05:46:46

[v2] 2014-12-31 02:45:55

[v3] 2015-04-30 10:33:05

[v4] 2015-05-01 04:33:25

[v5] 2015-05-20 11:16:57

[v6] 2015-06-05 02:16:20

[v7] 2015-06-12 16:10:45

[v8] 2015-06-17 11:59:17

[v9] 2015-06-27 03:07:27

[vA] 2015-07-28 04:51:49

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