# “Infinity, computability, and metamathematics: Celebrating the 60th birthdays of Peter Koepke and Philip Welch”

In the year 2014, Peter Koepke and Philip Welch are celebrating their 60th birthdays, and we wish to celebrate this festive occasion with a scientific workshop in their honor. Peter has been a professor at the University of Bonn for many years; Philip was a Mercator professor in Bonn during the academic year 2002/03.

## Friday, May 23

16:30 – 17:00 |
Coffee |

17:00 – 18:00 |
Joel Hamkins (New York): Colloquium |

## Saturday, May 24

10:00 – 10:50 |
Joan Bagaria (Barcelona) |

10:50 – 11:20 |
Coffee break |

11:20 – 12:10 |
Moti Gitik (Tel Aviv) |

12:10 – 14:30 |
Lunch break |

14:30 – 15:20 |
Ralf Schindler (Münster) |

15:20 – 15:50 |
Coffee break |

15:50 – 16:40 |
Heike Mildenberger (Freiburg) |

16:40 – 17:10 |
Coffee break |

17:10 – 18:00 |
Arthur Apter (New York) |

## Sunday, May 25

10:10 – 11:00 |
Jörg Brendle (Kobe) |

11:00 – 11:15 |
Coffee break |

11:15 – 12:05 |
Bernhard Schröder (Duisburg-Essen) |

12:05 – 12:10 |
Coffee break |

12:10 – 13:00 |
Adrian Mathias (Reunion) |

## Monday, May 26

16:30 – 18:00 |
Vladimir Kanovei (Moscow) |

Organizers: Stefan Geschke (Hamburg), Benedikt Löwe (Amsterdam & Hamburg), Philipp Schlicht (Bonn)

Venue: Mathematik-Zentrum, Lipschitz Lecture Hall, Endenicher Allee 60, Bonn

Registration: There is no registration fee. For more information please contact schlicht(at)math.uni-bonn.de

#### Abstracts:

#### Arthur Apter: Namba-like Forcings at Successors of Singular Cardinals

Following up on Peter Koepke’s CUNY Logic Workshop lecture of March 22, 2013, I will discuss Namba-like forcings which either exist or can be forced to exist at successors of singular cardinals.

#### Joan Bagaria: On hyper-stationary sets

We present some recent results on hyper-stationary subsets of regular cardinals. In particular, we shall look at (1) the connections between hyper-stationarity and second-order indescribability in the constructible universe, (2) the ideals associated to non-hyper-stationary sets, and (3) the consistency strength of hyper-stationarity.

#### Jörg Brendle: Cardinal invariants and highness properties

We present an analogy between cardinal invariants of the continuum from set theory and highness properties of Turing degrees from computability theory. In particular, we develop a version of Cichon’s diagram for highness properties and investigate to what extent results from set theory can be taken over to the computability context. This is joint work with Andrew Brooke-Taylor, Selwyn Ng, and Andre Nies.

#### Moti Gitik: Silver type theorems for collapses

The classical theorem of Silver states that GCH cannot break for the first time over a singular cardinal of uncountable cofinality. We would like to deal with the situation once blowing up power of singular cardinals is replaced by collapses of their successors.

#### Joel David Hamkins: Transfinite game values in infinite chess and other infinite games

I shall give a general introduction to the theory of infinite games, using infinite

chess—chess played on an infinite edgeless chessboard—as a central example. Since chess, when won, is won at a finite stage of play, infinite chess is an example of what is known technically as an open game, and such games admit the theory of transfinite ordinal game values. I shall exhibit several interesting positions in infinite chess with very high transfinite game values. The precise value of the omega one of chess is an open mathematical question.

#### Vladimir Kanovei: Automorphisms in the Gitik-Koepke construction

It is known that the assumption that GCH first fails at aleph omega implies in ZFC the existence of inner models with large cardinals. Gitik and Koepke demonstrated that this is not so without the axiom of choice. Namely there is a cardinal-preserving symmetric-generic extension of L, in which GCH holds at every cardinal aleph n but there is a surjection from the power set of aleph omega onto any previously chosen cardinal in L, as large as one wants, and the axiom of choice by necessity fails. In other words, in such an extension GCH holds in the proper sense for all cardinals aleph n but fails at aleph omega in Hartogs’ sense. The goal of this talk is to analyse the system of automorphisms involved in the Gitik-Koepke construction.

#### Adrian Mathias: Points of uncountable score

This talk will describe successful applications of descriptive set theory to symbolic dynamics, and list related open problems which might be similarly susceptible.

#### Heike Mildenberger: A simple P-aleph-1-point and a simple P-aleph-2-point

In the talk I will sketch a notion of forcing that establishes that it is consistent relative to ZFC that there a simple P-aleph-1-point and a simple P-aleph-2-point.

The main technical tool are iterands that destroy ultrafilters in one direction and preserve all P-points outside this direction. We will also clarify whether destruction means diagonalisation.

#### Ralf Schindler: Martin’s Maximum with an asterisk

We discuss whether Martin’s Maximum is consistent with or even implies Woodin’s axiom (*). This is joint work with D. Aspero and W. H. Woodin

#### Bernhard Schröder: How proofs are told. Text linguistics features of mathematical proofs

The talk will address the question to what extent text linguistic features can be identified in mathematical proof texts and what they could tell us about the communicative content and the cognitive representation of proofs.