|
|
|
| 1978 | Diploma, University of Bonn | | 1979 | Master of Arts, University of California, Berkeley, CA, USA | | 1984 | PhD, University of Freiburg | | 1984 - 1987 | Feodor-Lynen-Fellowship, Alexander von Humboldt Foundation, and | | Junior Research Fellow, Wolfson College, Oxford, England, UK | | 1987 - 1990 | Assistant Professor (C1), Habilitation, University of Freiburg | | 2014 | Visiting Fellow and Life Member, Clare Hall, Cambridge, UK | | Since 1990 | Professor (C3), University of Bonn |
|
|
My set theoretical research focusses around the construction and analysis of models of set theory with various combinatorial properties, using methods of forcing, inner models, and symmetric models. My main interest is on models having strong closure properties expressed by the existence of large cardinals like measurable and stronger cardinals. Model constructions allow to classify set theoretic properties in terms of large cardinals: A model with large cardinals is extended by forcing to a model of the combinatorial property; conversely assuming such a property one defines inner models of set theory with large cardinals.
The following questions are representative of my current research projects in axiomatic set theory: What remains of the ground model large cardinal properties in M. Gitik‘s model in which every cofinality is countable? What is the cardinal arithmetic of infinite sums and products in a model that I constructed with A. Fernengel ? How does Shelah's theory of possible cofinalities behave in that model? Can the model be modified so that the axiom of choice holds for countable families? I shall finalize work on the minimality of Prikry forcing with Gitik and Kanovei. The method of ordinal computability which I have developed will be employed in the fine structural analysis of Gödel‘s model of constructible sets.
In formal mathematics I shall further develop A. Paskevich‘s SAD system which is orientated towards natural mathematical language and argumentation. Based on previous experience with the Naproche system we are adding state-of-the-art natural language processing to SAD.
|
|
DFG project “Complexity and Definability at Higher Cardinals”
2015 - 2017
|
|
[ 1] Arthur W. Apter, Ioanna M. Dimitriou, Peter Koepke
All uncountable cardinals in the Gitik model are almost Ramsey and carry Rowbottom filters
MLQ Math. Log. Q. , 62: (3): 225--231
2016
DOI: 10.1002/malq.201400050[ 2] Arthur W. Apter, Ioanna M. Dimitriou, Peter Koepke
The first measurable cardinal can be the first uncountable regular cardinal at any successor height
MLQ Math. Log. Q. , 60: (6): 471--486
2014
DOI: 10.1002/malq.201110007[ 3] Moti Gitik, Peter Koepke
Violating the singular cardinals hypothesis without large cardinals
Israel J. Math. , 191: (2): 901--922
2012
DOI: 10.1007/s11856-012-0028-x[ 4] Peter Koepke, Julian J. Schlöder
The Gödel completeness theorem for uncountable languages
Formalized Mathematics , 20: : 199--203
2012[ 5] P. Koepke, P. D. Welch
Global square and mutual stationarity at the {\aleph_n}
Ann. Pure Appl. Logic , 162: (10): 787--806
2011
DOI: 10.1016/j.apal.2011.03.003[ 6] Peter Koepke
Turing computations on ordinals
Bulletin of Symbolic Logic , 11: (3): 377--397
2005[ 7] Peter Koepke
Extenders, embedding normal forms, and the Martin-Steel-theorem
J. Symbolic Logic , 63: (3): 1137--1176
1998
DOI: 10.2307/2586731[ 8] Sy D. Friedman, Peter Koepke
An elementary approach to the fine structure of L
Bull. Symbolic Logic , 3: (4): 453--468
1997
DOI: 10.2307/421099 |
|
|
|
|
|
|
|
| 2013 | CUNY Logic Workshop, New York, USA | | 2013 | Proof 2013, Bern, Switzerland | | 2013 | Mal'cev Meeting, Novosibirsk, Russia | | 2014 | 60th birthday conference of Philip Welch, Bristol, England, UK | | 2015 | Set Theory, Carnegie Mellon University, Pittsburgh, PA, USA | | 2015 | Philosophy of Mathematics Seminar, Oxford, England, UK | | 2015 | European Set Theory Conference, Cambridge, England, UK | | 2016 | Menachem Magidor 70th Birthday Conference, The Hebrew University of Jerusalem, Israel |
|
|
Heike Mildenberger (1998), now Professor, University of Freiburg
Benedikt Löwe (2005), now Professor, University of Amsterdam, Netherlands, and University of Hamburg
|
|
Ralf Schindler (1996): “The Core Model up to one Strong Cardinal”,
now Professor (C4), Mathematics, University of Münster
Merlin Carl (2011): “Alternative finestructural and computational approaches to constructibility”,
now Assistant Professor and Privatdozent, Mathematics, University of Konstanz
Benjamin Seyfferth (2013): “Three models of ordinal computability”,
now Coordinator of Studies, Mathematics, University of Darmstadt
Regula Krapf (2017): “Class forcing and second-order arithmetic”,
now Assistant Professor, Mathematics, University Koblenz-Landau
|
|
- Master theses: 9, currently 5
- Diplom theses: 60
- PhD theses: 11, currently 2
|
|
Download Profile  |
