Oberwolfach Seminar: New Trends in Gödelian Incompleteness and Combinatorics

Organizers

Harvey Friedman, Columbus

Antonio Montalban, Chicago

Michael Rathjen, Leeds

Andreas Weiermann, Gent

Date

October 16^th - October 22^nd, 2011

ID

1142b

Programme

A central question that has guided research during the last 40 years in Mathematical Logic is how Gödel's incompleteness phenomena relate to `ordinary' mathematical structures and practice. This research has provided the means to discover deep connections between areas which were hitherto thought to be unrelated. One such example was provided by linking Kruskal's tree theorem and the Robertson-Seymour graph minor theorem from combinatorics to the ordinal representations of proof theory.

In recent years this research found surprising connections between analytic combinatorics of finite trees and transfinite ordinals, and led to the study of phase transitions in independence results. The most striking examples of Gödelian incompleteness are provided by Harvey Friedman's Boolean Relation Theory and the very recent Kernel Theory, both concerning theorems about basic mathematical objects that can only be proved using more than the usual axioms for mathematics (ZFC).

The aim of this seminar is to fulfill the need of bringing the many different techniques together and present them to young researchers.

Prerequisites

Participants are expected to be comfortable with Gödel's incompleteness theorems and the basics of set theory and computability theory.

Literature

H. Friedman: Boolean relation theory and incompleteness, http://www.math.ohio-state.edu/~friedman/manuscripts.html

A. Montalban: Open questions in reverse mathematics, http://www.math.uchicago.edu/~antonio/papers/papers.html

M. Rathjen: The realm of ordinal analysis, in: S.B. Cooper and J.K. Truss (eds.), Sets and Proofs (Cambridge University Press, 1999) 219-279.

A. Weiermann: Phase transitions for Gödel incompleteness, Annals of Pure and Applied Logic 157 (2009) 281-296.

Deadline for applications

August 15^th, 2011

The seminars take place at the Mathematisches Forschungsinstitut Oberwolfach. The number of participants is restricted to 25. The Institute covers accommodation and food. We are pleased that the Carl Friedrich von Siemens Foundation has decided to support the Oberwolfach Seminars from summer 2008 to summer 2013. By this support, travel expenses can be reimbursed up to 200 Euro in average per person. Participants can ask for travel support during their stay in Oberwolfach at the guest office against copy of travel receipts. Applications including

• full name and address, including e-mail address
• present position, university
• name of supervisor of Ph.D. thesis
• a short summary of previous work and interest

should be sent preferably by e-mail (.ps or .pdf file) to:

    Prof. Dr. Dr. h.c. Gert-Martin Greuel
    Universität Kaiserslautern
    Fachbereich Mathematik
    Erwin Schrödingerstr.
    67663 Kaiserslautern, Germany