Location: MAGIC
Title: Ordering Ramsey Classes via the Modelling Property
NOTE room change: MAGIC
(Joint work with N. Meir) Generalised indiscernibles are one of the most useful tools in a model theorist's toolbox. Existence of generalised indiscernibles is closely connected with Ramsey's theorem, in a way made very explicit by Scow. In my talk will present and explain the basic background for generalised indiscernibles, Ramsey classes, and Scow's theorem. Then, I will discuss some techniques we recently introduced to generalise Scow's theorem, removing from it (almost) all technical assumptions. Finally, time permitting, I will mention how as an almost immediate corollary of our results, we obtain that every Ramsey class (not necessarily countable) admits a linear order which is the union of quantifier-free types.
Speaker's homepage
Location: MALL
Title: Weak o-minimality
A structure expanding a dense linear order is weakly o-minimal if any definable set in one variable is a finite union of points and convex sets. This is a more general condition compared to regular o-minimality, where we require these sets to be a finite union of points and intervals.
As a result, weak o-minimality doesn't have all the useful properties that o-minimality has, for example it's not preserved under elementary equivalence, nor can we show that any definable function is piecewise monotone and continuous.
In this talk I'll highlight some of the nice properties o-minimal structures have, give examples of weakly o-minimal structures which break those properties, and then show how we can salvage weaker versions of the properties in a weakly o-minimal setting.
Most of this talk will be based on a paper by Dugald Macpherson, David Marker and Charles Steinhorn called "Weakly O-minimal structures and real closed fields".
Speaker's homepage
