

1978  Diploma, University of Bonn  1979  Master of Arts, University of California, Berkeley, CA, USA  1984  PhD, University of Freiburg  1984  1987  FeodorLynenFellowship, 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 stateoftheart natural language processing to SAD.


DFG project “Complexity and Definability at Higher Cardinals”
2015  2017


Research Area KL My main results in axiomatic set theory, with coauthors, deal with “small” measurable cardinals within the bounded Gitik model [1], model theoretic properties about the existence of elementary substructures with cardinality constraints [2] or forcing extensions in which measurable cardinals or successor cardinals of the ground model become singular ([3], [4]). Sometimes large cardinals can be eliminated: we construct models of set theory without the axiom of choice in which the generalized continuum hypothesis formulated by F. Hausdorff can be violated in rather arbitrary ways (with A. Fernengel).
I developed the theory of ordinal computability, combining Turing computability and uncountable set theory. Calibrating certain parameters of ordinal computability one obtains initial segments of Gödel's model of various heights. With A. Morozov I determined the segment corresponding to infinite time BlumShubSmale machines [5].
In formal mathematics, we improved an earlier formalization of Gödel‘s completeness theorem to arbitrary languages [6]. I participated in philosophical discussions on the future impact of computersupported formal mathematics. 


[ 1] 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): 471486 2014 DOI: 10.1002/malq.201110007[ 2] 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): 225231 2016 DOI: 10.1002/malq.201400050[ 4] Dominik Adolf, Arthur W. Apter, Peter Koepke
Singularizing successor cardinals by forcing Proc. Amer. Math. Soc. , 146: (3): 773783 2018[ 5] Peter Koepke, Andrei S. Morozov
The computational power of infinite time BlumShubSmale machines Algebra and Logic , 56: (1): 3762 2017[ 6] Peter Koepke, Julian J. SchlÃ¶der
The GÃ¶del completeness theorem for uncountable languages Formalized Mathematics , 20: : 199203 2012[ 7] Moti Gitik, Peter Koepke
Violating the singular cardinals hypothesis without large cardinals Israel J. Math. , 191: (2): 901922 2012 DOI: 10.1007/s118560120028x[ 8] P. Koepke, P. D. Welch
Global square and mutual stationarity at the {\aleph_n} Ann. Pure Appl. Logic , 162: (10): 787806 2011 DOI: 10.1016/j.apal.2011.03.003[ 9] Peter Koepke
Turing computations on ordinals Bulletin of Symbolic Logic , 11: (3): 377397 2005[ 10] Peter Koepke
Extenders, embedding normal forms, and the MartinSteeltheorem J. Symbolic Logic , 63: (3): 11371176 1998 DOI: 10.2307/2586731[ 11] Sy D. Friedman, Peter Koepke
An elementary approach to the fine structure of L Bull. Symbolic Logic , 3: (4): 453468 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 secondorder arithmetic”,
now Assistant Professor, Mathematics, University KoblenzLandau


 Master theses: 9, currently 5
 Diplom theses: 60
 PhD theses: 11, currently 2


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