Oberwolfach Seminar: New Trends in Gödelian Incompleteness and Combinatorics
- Harvey Friedman, Columbus
- Antonio Montalban, Chicago
- Michael Rathjen, Leeds
- Andreas Weiermann, Gent
- October 16th - October 22nd, 2011
- 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
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.
- Participants are expected to be comfortable with Gödel's
incompleteness theorems and the basics of set theory and computability
- H. Friedman: Boolean relation theory and incompleteness,
- 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.
- 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
67663 Kaiserslautern, Germany
Mathematisches Forschungsinstitut Oberwolfach
updated: November 30th, 2010