16-22 Oct 2011
Oberwolfach, Germany
Oberwolfach Seminar: New trends in Gödelian Incompleteness and Combinatorics
This Oberwolfach Seminar was announced recently on
http://www.mfo.de/programme/seminars/
Details:
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
<http://www.math.ohio-state.edu/%7Efriedman/manuscripts.html>
A. Montalban: Open questions in reverse mathematics,
http://www.math.uchicago.edu/~antonio/papers/papers.html
<http://www.math.uchicago.edu/%7Eantonio/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
<http://www.mathematik.uni-kl.de/%7Egreuel/en/>
Universität Kaiserslautern
Fachbereich Mathematik
Erwin Schrödingerstr.
67663 Kaiserslautern, Germany