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Preprint Number 99

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99. Ya'acov Peterzil
Returning to semibounded sets
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Submission date: 8 November 2007

Abstract:

An o-minimal expansion of an ordered vector space by bounded predicates is called a semi-bounded structure. It is shown that every sufficiently saturated such structure is either linear (hence a reduct of an ordered vector space) or, after a modification of the language, it has an elementary substructure in which every interval admits a definable real closed field.

As a result certain questions about definably compact groups can be reduced to either ordered vector spaces or expansions of real closed fields. Using the known results in these two settings, the number of torsion points in definably compact abelian groups in expansions of ordered groups is given. Pillay's Conjecture for such groups follows.

Mathematics Subject Classification: 03C64

Keywords and phrases: o-minimal, Pillay's Conjecture, semibounded, definably compact groups

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