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

2 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

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General Mathematics

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10.1007/s11856-010-0084-z

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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.",

author = "Assaf Hasson and Alf Onshuus and Ya'acov Peterzil",

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",

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AU - Onshuus, Alf

AU - Peterzil, Ya'acov

N1 - 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

PY - 2010/12/1

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N2 - 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.

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.

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Definable one dimensional structures in o-minimal theories

Abstract

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