Set Theory and Logic

1811 Submissions

[10] viXra:1811.0269 [pdf] submitted on 2018-11-17 13:14:25

Refutation of Superposition as Glue in Matita Theorem Prover

Authors: Colin James III
Comments: 2 Pages. © Copyright 2018 by Colin James III All rights reserved. Respond to the author by email at: info@ersatz-systems dot com.

We evaluate the substitution lemma for the successor function, smart application of inductive hypotheses, and proof traces of a complex example in the Matita standard library. Results are not tautologous, hence refuting superposition.
Category: Set Theory and Logic

[9] viXra:1811.0264 [pdf] submitted on 2018-11-17 18:17:31

Refutation of Metamath Theorem Prover

Authors: Colin James III
Comments: 2 Pages. © Copyright 2018 by Colin James III All rights reserved. Respond to the author by email at: info@ersatz-systems dot com.

We evaluate six conjectures and one theorem, as proffered by Metamath staff. The conjectures are not tautologous. The Tarski-Grothendieck theorem is also not tautologous. Metamath fails our analysis.
Category: Set Theory and Logic

[8] viXra:1811.0220 [pdf] submitted on 2018-11-14 18:40:03

Shorter Refutation of the Löb Theorem and Gödel Incompleteness by Substitution of Contradiction

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

Löb’s theorem □(□X→X)→□X and Gödel’s incompleteness as □(□⊥ →⊥)→□⊥ are refuted.
Category: Set Theory and Logic

[7] viXra:1811.0154 [pdf] submitted on 2018-11-09 08:30:47

Find the extra shape (In Russian)

Authors: V. A. Kasimov
Comments: 2 Pages. in Russian

First, the task will put you in a dead end. No figure clearly stands out from the total number more than others. It's not as easy as it may seem in the first seconds.
Category: Set Theory and Logic

[6] viXra:1811.0148 [pdf] replaced on 2018-11-14 07:22:11

Refutation of the Alleged Łukasiewicz Nightmare in Ł4 Logic: (◇p&◇q)→◇(p&q)

Authors: Colin James III
Comments: 2 Pages. © Copyright 2018 by Colin James III All rights reserved. Respond to the author by email at: info@ersatz-systems dot com.

In Prover9 the alleged Łukasiewicz nightmare of (◇p&◇q)→◇(p&q) is not tautologous. However, in Prover 9 the nightmare recast in one variable as (◇p&◇~p)→◇(p&~p) is tautologous. In Meth8/VŁ4, both propositions are tautologous. This speaks to Meth8/VŁ4, based on the corrected modern Square of Opposition as an exact bivalent system, opposed to Prover9, based on the uncorrected modern Square of Opposition as an inexact probabilistic vector space.
Category: Set Theory and Logic

[5] viXra:1811.0078 [pdf] submitted on 2018-11-05 15:44:40

Refutation of Behavioral Mereology

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

If P≤P′ and Q′≤Q, proposition <>P'P<>QP' = <>QP is equivalent to []P'P[]QP' = []QP and respectively not tautologies.
Category: Set Theory and Logic

[4] viXra:1811.0075 [pdf] submitted on 2018-11-05 20:42:06

Refutation of the Blok-Esakia Theorem for Universal Classes

Authors: Colin James III
Comments: 2 Pages. © Copyright 2018 by Colin James III All rights reserved. Respond to the author by email at: info@ersatz-systems dot com.

Grzegorczyk (gzr) algebras as used for support and the Blok-Esakia theorems are not confirmed as tautologies and hence refuted.
Category: Set Theory and Logic

[3] viXra:1811.0059 [pdf] submitted on 2018-11-04 19:11:29

Refutation of First-Order Continuous Induction on Real Closed Fields

Authors: Colin James III
Comments: 3 Pages. © Copyright 2018 by Colin James III All rights reserved. Respond to the author by email at: info@ersatz-systems dot com.

By mapping definitions, theorems, and propositions into Meth8/VŁ4, we refute the first-order continuous induction principle on real closed fields.
Category: Set Theory and Logic

[2] viXra:1811.0020 [pdf] submitted on 2018-11-01 10:35:55

New Axioms in the Set Theory

Authors: Antoine Balan
Comments: 2 pages, written in english

We propose three new axioms in set theory, axiomatising the measure theory of the Hilbert spaces.
Category: Set Theory and Logic

[1] viXra:1811.0018 [pdf] replaced on 2018-11-09 17:10:10

Elementary Set Theory Can Be Used to Prove Fermat's Last Theorem (FLT)

Authors: Phil A. Bloom
Comments: 3 Pages.

An open problem is proving FLT simply for each integral $n>2$. Our proof of FLT is based on our algebraic identity, denoted, {for convenience}, as $r^n+s^n=t^n$. For $n\geq1$ we relate $r,s,t>0$, each a different function of variables comprising $r^n+s^n=t^n$, with $x,y,z>0$ for which $x^n+y^n=z^n$ holds. We infer as true by \emph{direct argument} (not BWOC), for any given $n>2$, that $\{(x,y,z)|x,y,z\in\mathbb{Z},x^n+y^n=z^n\}=\{(r,s,t)|r,s,t\in\mathbb{Z},r^n+s^n=t^n\}$. In addition, we show, for $n>2$, that $\{(r,s,t)|r,s,t\in\mathbb{Z},r^n+s^n=t^n\}=\varnothing$. Thus, for $n\in\mathbb{Z},n>2$, it is true that $\{(x,y,z)|x,y,z\in\mathbb{Z},x^n+y^n=z^n\}=\varnothing$.
Category: Set Theory and Logic