Definable one dimensional structures in o-minimal theories

Assaf Hasson, Alf Onshuus, Ya'acov Peterzil

Research output: Contribution to journalArticlepeer-review


This is the first of two papers where we prove the Zil'ber trichotomy principle for one-dimensional structures definable in o-minimal ones. Here we prove: Let N be a definable structure in an o-minimal structure M, with dimM(N) = 1. If N is stable then it is necessarily 1-based. Along the way, we develop a fine intersection theory for definable curves in o-minimal structures.

Original languageEnglish
Pages (from-to)297-361
Number of pages65
JournalIsrael Journal of Mathematics
Issue number1
StatePublished - 2010

Bibliographical note

Funding Information:
∗ Supported by the EPSRC grant no. EP C52800X 1. ∗∗Partially supported by the EC FP6 through the Marie Curie Network MODNET (MRTN-CT-2004-512234). Received April 14, 2007 and in revised form January 21, 2009

ASJC Scopus subject areas

  • General Mathematics


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