Seminar: | Countable Borel Equivalence Relations |
Dozent: | Jeffrey Burdges |
Zeit/Ort: | Do 9–11 Uhr, SR 318, Eckerstr. 1 |
Tutorium: | Juan Diego Caycedo |
Vorbesprechung: | in der 1. Vorlesungswoche |
Web-Seite: | http://home.mathematik.uni-freiburg.de/caycedo/ |
Inhalt:
The sigma-algebra of Borel subsets of a complete separable metric space is
isomorphic to that obtained from either the reals, the integers, or a finite
set. The sigma-algebra of Borel subsets of the reals is known as the
standard Borel space X. We say a Borel equivalence relation E on
X is countable if every E-class is countable. All countable Borel
equivalence relations are orbit equivalence relations arising from a
countable discrete groups acting upon the standard Borel space, although
expressing an arbitrary equivalence relation naturally may prove
difficult.
A great many interesting mathematical problems are reducible to countable Borel equivalence relations. Borel reductions then provide a rich theory for comparing the relative difficulty of many classical problems in mathematics. For example, any countable Borel equivalence relation is reducible to the isomorphism problem for finitely generated groups.
Literatur:
______________________________________________________________________________________________Typisches Semester: | 6. Semester |
Studienschwerpunkt: | Mathematische Logik |
Notwendige Vorkenntnisse: | Modelltheorie |
Sprechstunde Dozent: | nach Vereinbarung, Eckerstr. 1 |
Sprechstunde Assistent: | nach Vereinbarung, Zi. 304, Eckerstr. 1 |