Definable structures in o-minimal theories: One dimensional types

Assaf Hasson, Alf Onshuus, Ya'acov Peterzil

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Let N be a structure definable in an o-minimal structure M and p ∈ SN (N), a complete N-1-type. If dimM(p) = 1, then p supports a combinatorial pre-geometry. We prove a Zilber type trichotomy: Either p is trivial, or it is linear, in which case p is non-orthogonal to a generic type in an N-definable (possibly ordered) group whose structure is linear, or, if p is rich then p is non-orthogonal to a generic type of an N-definable real closed field. As a result, we obtain a similar trichotomy for definable one-dimensional structures in o-minimal theories.

Original languageEnglish
Pages (from-to)363-379
Number of pages17
JournalIsrael Journal of Mathematics
Volume179
Issue number1
DOIs
StatePublished - 1 Dec 2010
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics (all)

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