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Friday, September 5, 2008

Model Theory and Descriptive Set Theory
4:00 pm   in 347 Altgeld Hall,  Friday, September 5, 2008
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Submitted by vlopes2.
Isaac Goldbring (UIUC Math)
Randomizations of Structures and the Search for a Well-Behaved Unstable Continuous Theory
Abstract: In this talk, I will give an introduction to the notion of a randomization of a first-order structure, where one builds a metric structure out of the "random variables" of a classical first-order structure. The theory of the randomization of a structure turns out to be axiomatizable and shares many of the model-theoretic properties of the original structure (e.g. omega-categoricity, omega-stability, stability, NIP). In his search for an essentially continuous simple unstable theory, Itai Ben-Yaacov hoped that the randomization of a simple unstable theory would be simple unstable. However, this is not the case and I hope to present his proof of this fact. I will end with the statement of a naive conjecture that randomizations of rosy theories might be rosy.