皆様：

神戸大学の酒井拓史と申します． 8月1日(水)に開催される Kobe Colloquium on Logic, Statistics and Informatics のアナウンスをさせていただきます． ご興味をお持ちの方は是非ご参加ください：

------------------------------------------------------ Kobe Colloquium on Logic, Statistics and Informatics: ------------------------------------------------------ August 1, 2012 (Wed.) 16:30 - 18:00 (teabreak: 15:30 -)

``Topological Set Theory''

Dr. Andreas Fackler (LMU Munich)

Abstract

The idea behind positive set theory is to weaken the naive comprehension principle by omitting all instances in which negation occurs. For example, the universal class V is a set while the Russell class is not. Surprisingly, this approach leads to a theory in which V is a topological space in a natural way.

Inspired by that fact, topological set theory TS instead of a comprehension principle has as its axioms several topological statements about V. Topological and positive set theory are closely related and in both of them there is an interesting interplay between the set theoretic and topological properties of V. Many basic theorems of TS remain true even without the axiom that the universal class V is a set, although one decisive statement about the ordinal numbers goes missing. Instead, a surprising connection to another familiar set theory arises ...

In my talk, I will present this family of axiom systems and give an overview of results about their implications, their consistency strengths, and their interrelations. We will also look briefly at their (known) models -- topological structures called hyperuniverses -- and at methods to construct such objects. ------------------------------------------------------------------------------ The talk will be given in the presentation room of the group of Logic, Statistics and Informatics (inside the glass door with "Fuchino group" (written in Japanese) on the 4th floor in the Sience and Technology Building 3 http://kurt.scitec.kobe-u.ac.jp/~brendle/Forcing2012/university.jpg in Rokkodai Campus of Kobe University)

There will be a dinner after the talk.

酒井 拓史 神戸大学大学院 システム情報学研究科 講師 e-mail: [email protected] tel: 078-803-6245