Prof. Dr. Benjamin Miller
Institut für Mathematische Logik und Grundlagenforschung
| ben dot miller at uni-muenster dot de | |
| Telefon | +49 251 83-32685 |
| FAX | +49 251 83-33078 |
| Zimmer | 815a |
| Sekretariat | Sekretariat Pfeifer Telefon +49 251 83-33790 Fax +49 251 83-33078 Zimmer 811 |
| Adresse | Prof. Dr. Benjamin Miller Institut für Mathematische Logik und Grundlagenforschung Fachbereich Mathematik und Informatik der Universität Münster Einsteinstrasse 62 48149 Münster Deutschland |
Conferences
MALOA Set Theory Research Workshop.Courses
Introductory forcing seminar.Logik IV.
Oberseminar.
Notes
Isomorphism via full groups.Density of topological full groups.
A simple marriage problem.
A weak reducibility lemma.
A reducibility lemma.
A dichotomy theorem for graphs induced by commuting families of Borel injections.
A generalized marker lemma.
The axiom of dependent choice and regular open algebras of Baire spaces.
The dual Schröder-Bernstein theorem and Borel equivalence relations.
Baire measurable matchings in acyclic locally finite Borel graphs. With Clinton Conley.
Baire measurable 3-colorings in acyclic locally finite Borel graphs. With Clinton Conley.
An antibasis result for graphs of infinite Borel chromatic number. With Clinton Conley.
Publications
Topics in orbit equivalence. With Alexander Kechris. Lecture notes in mathematics, 1852, Springer, 2004.Coordinatewise decomposition, Borel cohomology, and invariant measures. Fundamenta Mathematicae, 81-94, 191 (1), 2006.
Isomorphism of Borel full groups. With Christian Rosendal. Proceedings of the American Mathematical Society, 517-522, 135 (2), 2007.
Coordinatewise decomposition of group-valued Borel functions. Fundamenta Mathematicae, 119-126, 196 (2), 2007.
Means on equivalence relations. With Alexander Kechris. Israel Journal of Mathematics, 241-263, 163, 2008.
The existence of quasi-invariant measures of a given cocycle, I: Atomless, ergodic sigma-finite measures. Ergodic Theory and Dynamical Systems, 1599-1613, 28 (5), 2008.
The existence of quasi-invariant measures of a given cocycle, II: Probability measures. Ergodic Theory and Dynamical Systems, 1615-1633, 28 (5), 2008.
Measurable chromatic numbers. Journal of Symbolic Logic, 1139-1157, 73 (4), 2008.
Ends of graphed equivalence relations, I. Israel Journal of Mathematics, 375-392, 169, 2009.
Ends of graphed equivalence relations, II. With Greg Hjorth. Israel Journal of Mathematics, 393-415, 169, 2009.
Descriptive Kakutani equivalence. With Christian Rosendal. Journal of the European Mathematical Society, 179-219, 12 (1), 2010.
Basis theorems for non-potentially closed sets and graphs of uncountable Borel chromatic number. With Dominique Lecomte. Journal of Mathematical Logic, 121-162, 8 (2), 2008.
The Kanovei-Zapletal canonization. To appear in the Proceedings of the 2009 Boise Extravaganza in Set Theory.
Dichotomy theorems for countably-infinite dimensional analytic hypergraphs. To appear in the Proceedings of the Logic Colloquium 2009.
Definability of small puncture sets. With Andres Caicedo, John Clemens, and Clinton Conley. To appear in Fundamenta Mathematicae.
Slides
Slides from Luminy.Slides from Paris.
Slides from Singapore.
Unpublished work
Paris lectures: Introduction.Paris lectures: Silver's theorem.
Paris lectures: Hjorth's theorem.
Paris lectures: The Harrington-Kechris-Louveau theorem.
Paris lectures: The Kanovei-Louveau theorem.
Borel equivalence relations and everywhere faithful actions of free products.
The classification of finite Borel equivalence relations on the hyperfinite quotient space.
On the existence of invariant probability measures for Borel actions of countable semigroups.
An anti-basis theorem for analytic graphs of Borel chromatic number at least three.
Definable transversals of analytic equivalence relations.
Lecture notes on Borel dynamics.
Borel homomorphisms of smooth sigma-ideals. With John Clemens and Clinton Conley.
Defining non-empty small sets from families of finite sets. With Andres Caicedo, John Clemens, and Clinton Conley.
Descriptive set-theoretic dichotomy theorems and limits superior. With Clinton Conley and Dominique Lecomte.
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