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Groups, measures, and the NIP

- E. Hrushovski, Y. Peterzil, A. Pillay
- Mathematics
- 18 July 2006

We discuss measures, invariant measures on definable groups, and genericity, often in an NIP (failure of the independence property) environment. We complete the proof of the third author’s… Expand

173 12- PDF

Definability of restricted theta functions and families of abelian varieties

- Y. Peterzil, S. Starchenko
- Mathematics
- 16 March 2011

We consider some classical maps from the theory of abelian varieties and their moduli spaces and prove their definability, on restricted domains, in the o-minimal structure $\Rae$. In particular, we… Expand

46 10- PDF

Definable Compactness and Definable Subgroups of o‐Minimal Groups

- Y. Peterzil, C. Steinhorn
- Mathematics
- 1 June 1999

The paper introduces the notion of definable compactness and within the context of o-minimal structures proves several topological properties of definably compact spaces. In particular a definable… Expand

124 8

A trichotomy theorem for o-minimal structures

- Y. Peterzil, S. Starchenko
- Mathematics
- 1 November 1998

Let M kM; <; . . . l be a linearly ordered structure. We de®ne M to be o-minimal if every de®nable subset of M is a ®nite union of intervals. Classical examples are ordered divisible abelian groups… Expand

73 8- PDF

Definably simple groups in o-minimal structures

- Y. Peterzil, A. Pillay, S. Starchenko
- Mathematics
- 24 February 2000

Let G = 〈G, ·〉 be a group definable in an o-minimal structure M. A subset H of G is G-definable if H is definable in the structure 〈G, ·〉 (while definable means definable in the structure M). Assume… Expand

71 8- PDF

Linear O-minimal structures

- James Loveys, Y. Peterzil
- Mathematics
- 1 February 1993

AbstractA linearly ordered structure
$$\mathcal{M} = (M,< , \cdot \cdot \cdot )$$
is called o-minimal if every definable subset ofM is a finite union of points and intervals. Such an
$$\mathcal{M}$$… Expand

41 6

Quasi-o-minimal structures

- O. Belegradek, Y. Peterzil, F. Wagner
- Computer Science, Mathematics
- Journal of Symbolic Logic
- 1 September 2000

TLDR

41 6

On Groups and Rings Definable In O–Minimal Expansions of Real Closed Fields

- M. Otero, Y. Peterzil, A. Pillay
- Mathematics
- 1996

Let 〈R,<,+, ·〉 be a real closed field and let M be an o-minimal expansion of R. We prove here several results regarding rings and groups which are definable in M. We show that every M-definable ring… Expand

42 6- PDF

Generic sets in definably compact groups

- Y. Peterzil, A. Pillay
- Mathematics
- 2007

A subset X of a group G is called left-generic if finitely many left-translates of X cover G. Our main result is that if G is a definably compact group in an o-minimal structure and a definable X ⊆ G… Expand

38 5- PDF

THE CENTRAL PATH IN SMOOTH CONVEX SEMIDEFINITE PROGRAMS

- L. M. Graña Drummond, Y. Peterzil
- Mathematics
- 1 April 2002

Abstract In this paper we study the welldefinedness of the central path associated to a nonlinear convex semidefinite programming problem with smooth objective and constraint functions. Under… Expand

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