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Preprint Number 100

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100. Ya'acov Peterzil
Pillay's Conjecture and its solution-a survey
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Submission date: 8 November 2007

Abstract:

Pillay's Conjecture has been a strong driving force behind a large body of work in recent years. Its beauty is in the fact that it makes a surprising connection between the lattice of definable sets in definable groups in arbitrary o-minimal structures and compact real Lie groups. The relationship between the two is modeled after a similar connection between compact real Lie groups and their elementary extensions. The proof of the conjecture makes use of a variety ot techniques from o-minimality, abstract model theory, group theory, measure theory and more.

In this survey I give an almost complete proof of Pillay's Conjecture for expansions of real closed fields, extracted from several different papers, where the results were originally published.

Mathematics Subject Classification: 03C64, 03C45

Keywords and phrases: o-minimal, Pillay's Conjecture, Keisler measure, definably compact groups, NIP

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