# Set Theory and Logic

## 1506 Submissions

[3] **viXra:1506.0165 [pdf]**
*replaced on 2018-12-11 01:44:49*

### Boolean Algebra and Propositional Logic

**Authors:** Takahiro Kato

**Comments:** 16 Pages.

In this article, we present yet another characterization of Boolean algebras and, using this characterization, establish a connection between propositional logic and Boolean algebras; in particular, we derive a deductive system for propositional logic starting with 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 2017-02-15 03:38:49*

### Non-Archimedean Analysis on the Extended Hyperreal Line ∗R_d and the Solution of Some Very Old Transcendence Conjectures Over the Field Q.

**Authors:** Jaykov Foukzon

**Comments:** 84 Pages.

In 1980 F. Wattenberg constructed the Dedekind completion∗d of the Robinson
non-archimedean field ∗ and established basic algebraic properties of ∗d [6]. In
1985 H. Gonshor established further fundamental properties of ∗d [7].In [4]
important construction of summation of countable sequence of Wattenberg numbers
was proposed and corresponding basic properties of such summation were
considered. In this paper the important applications of the Dedekind completion∗d in
transcendental number theory were considered. We dealing using set theory
ZFC ∃(-model of ZFC).Given an class of analytic functions of one complex
variable f ∈ z, we investigate the arithmetic nature of the values of fz at
transcendental points en,n ∈ ℕ. Main results are: (i) the both numbers e and e
are irrational, (ii) number ee is transcendental. Nontrivial generalization of the
Lindemann- Weierstrass theorem is obtained.

**Category:** Set Theory and Logic