# Set Theory and Logic

## 1005 Submissions

[2] **viXra:1005.0059 [pdf]**
*replaced on 22 Nov 2010*

### Geometrical Axioms Refuting the Continuum-Hypothesis

**Authors:** Dm. Vatolin

**Comments:** 14 pages, Russian.

This article formulates three geometrical axioms from which it follows
that the continuum power is greater then any well-ordered set power.

**Category:** Set Theory and Logic

[1] **viXra:1005.0006 [pdf]**
*submitted on 10 Mar 2010*

### Neutrality and Many-Valued Logics

**Authors:** Andrew Schumann, Florentin Smarandache

**Comments:** 121 pages

This book written by A. Schumann & F. Smarandache is devoted to advances
of non-Archimedean multiple-validity idea and its applications to logical reasoning.
Leibnitz was the first who proposed Archimedes' axiom to be rejected.
He postulated infinitesimals (infinitely small numbers) of the unit interval [0, 1]
which are larger than zero, but smaller than each positive real number. Robinson
applied this idea into modern mathematics in [117] and developed so-called
non-standard analysis. In the framework of non-standard analysis there were
obtained many interesting results examined in [37], [38], [74], [117].

**Category:** Set Theory and Logic