Set Theory and Logic

1802 Submissions

[3] viXra:1802.0357 [pdf] submitted on 2018-02-25 07:56:34

P=NP Resolution, with 3-Sat not Tautologous © Copyright 2017-2018 by Colin James III All Rights Reserved.

Authors: Colin James III
Comments: 3 Pages. © Copyright 2017-2018 by Colin James III All rights reserved.

We use the definition of NP as “nondeterministic polynomial time” from Stephen Cook at claymath.org/sites/default/files/pvsnp.pdf. It is not tautologous and is presented in a truth table on 1024-values. An example from the same source for the 3-SAT test as NP-complete for the expression (p∨q∨r)∧(~p∨q∨~r)∧(p∨~q∨s)∧(~p∨~r∨~s), with τ(P)=τ(Q)=Tautologous and τ(R)=τ(S)=contradictory, is not tautologous.
Category: Set Theory and Logic

[2] viXra:1802.0329 [pdf] submitted on 2018-02-22 14:00:52

Refutation of the ef-Axiom © Copyright 2018 by Colin James III All Rights Reserved.

Authors: Colin James III
Comments: 1 Page. © Copyright 2018 by Colin James III All rights reserved.

The EF-axiom describes the Efremovifč proximity δ by V.A. Efremovič from 1934 and published in Russian in 1951. We interpret the operator δ to mean "nearby" or "in proximity". The size of an antecedent or consequent is not stated for the operator, so we determine that the operator applies to unrelated literals as as ((A∈ B) Nor (B∈ A)). The proof result is for 256-values because four theorems are evaluated as variables. We find the EF-axiom is not tautologous. The implications to topology are legion.
Category: Set Theory and Logic

[1] viXra:1802.0172 [pdf] submitted on 2018-02-14 06:16:03

Refutation of Tarski's Undefinability of Truth Theorem © Copyright 2018 by Colin James III All Rights Reserved.

Authors: Colin James III
Comments: 1 Page. © Copyright 2018 by Colin James III All rights reserved.

This refutes Tarski's theorem for the undefinability of truth as: "no definable and sound extension of Peano Arithmetic can be complete"; or in abstract terms, "the proof of a system cannot be demonstrated by itself". Tarski's theorem is an arguable equivalent to Godel's incompleteness theorem, as based on the liar's paradox. [Remark added later: Tarski's theorem as used since about 1936 is an underpinning of quantum theory and a universal justification for atheism.]
Category: Set Theory and Logic