Definable one dimensional structures in o-minimal theories

Assaf Hasson; Alf Onshuus; Ya'acov Peterzil

doi:10.1007/s11856-010-0084-z

Definable one dimensional structures in o-minimal theories

Assaf Hasson
, Alf Onshuus
, Ya'acov Peterzil

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

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 dim_M(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 language	English
Pages (from-to)	297-361
Number of pages	65
Journal	Israel Journal of Mathematics
Volume	179
Issue number	1
DOIs	https://doi.org/10.1007/s11856-010-0084-z
State	Published - 1 Dec 2010
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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abstract = "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.",

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AU - Peterzil, Ya'acov

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AB - 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.

UR - https://www.scopus.com/pages/publications/80054873642

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Definable one dimensional structures in o-minimal theories

Abstract

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