Interpretable groups are definable-Reference-Cited by-同舟云学术

Interpretable groups are definable

Published:2014-06 Issue:01 Volume:14 Page:1450002
ISSN:0219-0613
Container-title:Journal of Mathematical Logic
language:en
Short-container-title:J. Math. Log.

Author:

Eleftheriou Pantelis E.¹,Peterzil Ya'acov²,Ramakrishnan Janak³

Affiliation:

1. Department of Mathematics and Statistics, University of Konstanz, Zukunftskolleg, Box 216, 78457 Konstanz, Germany

2. Department of Mathematics, University of Haifa, Mount Carmel, Haifa 31905, Israel

3. Google, Inc., 76 9th Ave, New York, NY 10011, USA

Abstract

We prove that in an arbitrary o-minimal structure, every interpretable group is definably isomorphic to a definable one. We also prove that every definable group lives in a cartesian product of one-dimensional definable group-intervals (or one-dimensional definable groups). We discuss the general open question of elimination of imaginaries in an o-minimal structure.

Publisher

World Scientific Pub Co Pte Lt

Subject

Logic

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219061314500020

Reference20 articles.

1. Solvable groups definable in o-minimal structures

2. DEFINABLY COMPACT ABELIAN GROUPS

3. Local analysis for semi-bounded groups

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