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Preprint Number 99
99. Ya'acov Peterzil Returning to semibounded sets Email: Submission date: 8 November 2007 Abstract: An ominimal expansion of an ordered vector space by bounded predicates is called a semibounded 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: ominimal, Pillay's Conjecture, semibounded, definably compact groups Full text: pdf.

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