# Set Theory and Logic

## 1506 Submissions

[3] **viXra:1506.0165 [pdf]**
*replaced on 2015-09-10 05:47:49*

### Boolean Algebra and Propositional Logic

**Authors:** Takahiro Kato

**Comments:** 16 Pages.

This article provides yet another characterization of Boolean algebras and, using this characterization, establishes a more direct connection between propositional logic and Boolean algebras.

**Category:** Set Theory and Logic

[2] **viXra:1506.0147 [pdf]**
*replaced on 2015-07-26 23:12:31*

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

**Authors:** Thomas Colignatus

**Comments:** 13 Pages.

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.

**Category:** Set Theory and Logic

[1] **viXra:1506.0145 [pdf]**
*replaced on 2016-05-14 14:11:23*

### The Solution of Some Very Old Transcendence Conjectures Over the Field Q by Using Algebra of Dedekind Hyperreals

**Authors:** Jaykov Foukzon

**Comments:** 61 Pages. Advances in Pure Mathematics Vol.5 No.10, Pub. Date: August 19, 2015

In this paper the important applications of the Dedekind completion *R_d in transcendental number theory is considered. We dealing using set theory ZFC+~∃(omega-model of ZFC).Given an class of analytic functions of one complex variable f ∈Q[[z]],we investigate the arithmetic nature of the values of f(z) at transcendental points e^n. Main results are: (i) the both numbers e+pi and e-pi are irrational, (ii) number e^e are transcendental. Nontrivial generalization of the Lindemann-Weierstrass theorem is obtained.

**Category:** Set Theory and Logic