Set Theory and Logic

1808 Submissions

[3] viXra:1808.0090 [pdf] submitted on 2018-08-07 15:06:59

Refutation of Lean Theorem Prover from Microsoft

Authors: Colin James III
Comments: 1 Page. Copyright © 2018 by Colin James III All rights reserved. Respond to this author's email address: info@ersatz-systems dot com. (We instruct troll Mikko at Disqus to read the entire article twice before she starts typing.)

These examples were found not tautologous: (∀x,px→r)↔(∃x,px)→r; (∃x,px→r)↔(∀x,px)→r; (∃x,r→px)↔(r→∃x,px). Hence Lean prover from Microsoft is not bivalent and refuted.
Category: Set Theory and Logic

[2] viXra:1808.0047 [pdf] submitted on 2018-08-03 22:08:52

Shortest Refutations of the Zermelo-Fraenkel (ZF) Axioms

Authors: Colin James III
Comments: 4 Pages. Copyright © 2018 by Colin James III All rights reserved. Note that comments on Disqus are not forwarded or read, so respond to this author's email address: info@ersatz-systems dot com .

The nine Zermelo-Fraenkel (ZF) axioms evaluated are not tautologous.
Category: Set Theory and Logic

[1] viXra:1808.0034 [pdf] replaced on 2018-08-04 08:07:43

Shortest Refutation of the Zermelo-Fraenkel (ZF) Axiom of the Empty Set

Authors: Colin James III
Comments: 1 Page. Copyright © 2018 by Colin James III All rights reserved. Respond to this author's email address: info@ersatz-systems dot com .

A possible set contains no necessary element: not tautologous. Furthermore, the empty set cannot be a subset of another set.
Category: Set Theory and Logic