[FOM] Oberwolfach Seminar October 2011

[Harvey Friedman]

Oberwolfach Seminar:

New Trends in Goedelian 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 Goedel'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  
Goedelian 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  
Goedel'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 Goedel 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