Kurt Gödel Research Center

2012 seminar talk: Reducts of the random partial order

Talk held by Michael Pinsker (Paris 7, France, TU Wien, Austria, and Hebrew University of Jerusalem, Israel) at the KGRC seminar on 2012-03-01.

Abstract

I will present a recent result which states that up to first-order interdefinability, there exist precisely 5 structures which are first-order definable in the universal homogeneous partial order. I will also outline the proof of this result, which is achieved by finding all closed permutation groups which contain the automorphism group of this order. The method for finding the groups relies on a Ramsey-theoretic analysis of permutations acting on the order, which makes it possible to find regular patterns in such permutations and make them accessible to finite combinatorial arguments.