Probability Axioms and Set Theory Paradoxes

Quantum Mechanics: Structures, Axioms and Paradoxes∗

We present an analysis of quantum mechanics and its problems and paradoxes taking into account the results that have been obtained during the last two decades by investigations in the field of ‘quantum structures research’. We concentrate mostly on the results of our group FUND at Brussels Free University. By means of a spin 1 2 model where the quantum probability is generated by the presence o...

Cantor’s Grundlagen and the Paradoxes of Set Theory

Foundations of a General Theory of Manifolds [Cantor, 1883], which I will refer to as the Grundlagen, is Cantor’s first work on the general theory of sets. It was a separate printing, with a preface and some footnotes added, of the fifth in a series of six papers under the title of “On infinite linear point manifolds”. I want to briefly describe some of the achievements of this great work. But ...

Partial Universes and the Axioms of Set Theory

This paper is intended as a senior thesis. The topic is set theory. The material covered is not particularly advanced with respect to the field. However, this author has never had the opportunity to take an official class in set theory; it was in the course of preparing this document that he himself was introduced to set theory. After introducing some fundamental notions from set theory and log...

Forcing axioms and inner models of set theory

Axioms and Models for an Extended Set Theory

We present the axioms of extended set theory (XST) and the ideas underlying the axioms. We also present an interpretation of XST in ZFC plus “there exist arbitrarily large inaccessible cardinals,” thereby proving the consistency of XST relative to this mild large-cardinal extension of ZFC.