Oberseminar Mathematische Logik
Advanced talks on mathematical logic by guests and members of the logic group.
Organized by
- Prof. Dr. Peter Koepke
- Prof. Dr. Stefan Geschke
- Dr. Philipp Schlicht
Time and location
Thursdays 10.15-11.45 at room 1.007, Endenicher Allee 60. The participants are welcome to join for lunch after the talk.
Contents
As usual, there will be several invited talks. In the talks by members of the logic group, we will focus on walks on ordinals and their applications. For more information see Stevo Todorcevic: Walks on Ordinals and Their Characteristics, Birkhäuser 2007.
Programme
- 18 April (Monday 14.15-15.45 at Lipschitz-Saal 1.016) Ralf Schindler (Universität Münster) Resectionable truth
- Which consistent statements can be forced to be true? It is shown that "resectionable" Sigma_1 statements about parameters in H_omega_2 which are consistent in a strong sense can be forced to be true in a stationary set preserving extension. We also give some applications.
- 21 April meeting was postponed
- 28 April Peter Koepke Coherent sequences and walks on ordinals
- 05 May Jan Reimann (Penn State University) Old and new results on algorithmic equivalence relations
- Borel equivalence relations arising from recursion theoretic reducibilities seem to exhibit a stubborn resistance to complete classification. One reason may be seen in the fact that they relate to deep recursion theoretic problems, first and foremost Martin's Conjecture on degree invariant functions. I will present some recent progress on the classification of several recursion theoretic equivalence relations.
- 12 May Peter Koepke Coherent sequences and walks on ordinals (continued)
- 19 May Stefan Geschke The square bracket operation on a special Aronszajn tree
- 26 May Katie Thompson (Vienna University of Technology) Bounding and domination for the embedding structure of bounded kappa-trees
- 30 May (Monday 10.15-11.45) Philipp Schlicht Aronszajn trees and coherent maps
- 09 June Thilo Weinert Partition relations on countable ordinals
- In the fifties Erdős and Rado introduced the partition calculus. The partition relation alpha --> (beta, gamma)^n is nowadays mainly known through results for finite values of alpha, beta and gamma, e.g. through the theorem about friends and strangers, for example in its simplest case, 6 --> (3, 3)^2. For n = 2, gamma natural and alpha, beta countable there have been several results by Erdős, Rado, Specker, Chang, Milner, Larson, Nosal, Schipperus and Darby. Most of these results have been concerned with the special case where alpha = beta. For beta and gamma both given, a finitary characterization of the smallest alpha such that alpha --> (beta, gamma)^2 holds true was known for beta either a finite multiple or a finite power of omega. We are going to analyze this problem for beta a finite multiple of omega^2 and give a characterization in terms of finite 3-coloured directed graphs. We are also going to compute the smallest example, i.e. the Ramsey number for omega^2 * 2 and 3.
- 10 June (Friday 14.15, Lipschitz-Saal 1.016) Merlin Carl's Doctoral defense
- 16 June no seminar (Pfingsten)
- 20 June (Monday 10.15-11.45 in room 1.007) Philipp Schlicht Walks on ordinals and gaps
- 30 June Robert Lubarsky (Florida Atlantic University) Independence Results in Reverse Constructive Mathematics
- In recent years, subtle variants of foundational principles have been identified and shown to be of some practical importance. It is therefore of interest to know whether apparently different principles are actually equivalent to each other or not. We will show the inequivalence of some of these, using techniques that should be familiar from classical set theory.
- 01 July (Friday 10.15-11.45 in room 1.007) Grigori Mints (Stanford) Extension of Epsilon Substitution to Second Order Systems
- The problem of extending epsilon substitution method to second order systems was posed by Hilbert in 1928 and repeated in "Grundlagen der Mathematik" (1939). In this talk I will remind some history, describe the first order formulation (due to Hilbert, Ackermann von Neumann and Bernays) from "Grundlagen der Mathematik", outline possible extensions to the second order, progress achieved up to now and obstacles to termination proof.