[FOM] Oberwolfach Seminar: New trends in G"odelian Incompleteness and Combinatorics

[Andreas Weiermann]

OBERWOLFACH SEMINAR: NEW TRENDS IN GÖDELIAN INCOMPLETENESS AND COMBINATORICS

Organizers
Harvey Friedman, Columbus
Antonio Montalban, Chicago
Michael Rathjen, Leeds
Andreas Weiermann, Gent
Date
October 16th - October 22nd, 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 15th, 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






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