Set Theory and Logic

1005 Submissions

[2] viXra:1005.0059 [pdf] replaced on 2017-06-04 03:19:45

Geometric Axioms Entailing the Negation of the Continuum Hypothesis

Authors: Vatolin Dm.
Comments: 14 Pages. Russian

In the article formulated are the geometric axioms from which it follows that the continuum power is more than the power of any well-ordered set.
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