Interpretable groups are definable

Pantelis E. Eleftheriou; Ya'Acov Peterzil; Janak Ramakrishnan

doi:10.1142/S0219061314500020

Interpretable groups are definable

Pantelis E. Eleftheriou, Ya'Acov Peterzil, Janak Ramakrishnan

Department of Mathematics

University of Haifa

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

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.

Original language	American English
Article number	1450002
Journal	Journal of Mathematical Logic
Volume	14
Issue number	1
DOIs	https://doi.org/10.1142/S0219061314500020
State	Published - Jun 2014

Keywords

definable groups
elimination of imaginaries
interpretable groups
o-minimality

All Science Journal Classification (ASJC) codes

Logic

Access to Document

10.1142/S0219061314500020

Cite this

@article{538079431ca04e319cba647904152b1e,

title = "Interpretable groups are definable",

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.",

keywords = "definable groups, elimination of imaginaries, interpretable groups, o-minimality",

author = "Eleftheriou, {Pantelis E.} and Ya'Acov Peterzil and Janak Ramakrishnan",

note = "Funding Information: The authors thank M{\'a}rio Edmundo and the FCT grant PTDC/MAT/101740/2008 for bringing them together in Lisbon, where this work was begun. They also thank the referee for the careful reading of the paper. The first author is supported by the EU FP7 Marie Curie Zukunftskolleg Incoming Fellowship Programme, University of Konstanz (grant no. 291784).",

year = "2014",

month = jun,

doi = "10.1142/S0219061314500020",

language = "American English",

volume = "14",

journal = "Journal of Mathematical Logic",

issn = "0219-0613",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "1",

}

TY - JOUR

T1 - Interpretable groups are definable

AU - Eleftheriou, Pantelis E.

AU - Peterzil, Ya'Acov

AU - Ramakrishnan, Janak

N1 - Funding Information: The authors thank Mário Edmundo and the FCT grant PTDC/MAT/101740/2008 for bringing them together in Lisbon, where this work was begun. They also thank the referee for the careful reading of the paper. The first author is supported by the EU FP7 Marie Curie Zukunftskolleg Incoming Fellowship Programme, University of Konstanz (grant no. 291784).

PY - 2014/6

Y1 - 2014/6

N2 - 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.

AB - 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.

KW - definable groups

KW - elimination of imaginaries

KW - interpretable groups

KW - o-minimality

UR - http://www.scopus.com/inward/record.url?scp=84903594514&partnerID=8YFLogxK

U2 - 10.1142/S0219061314500020

DO - 10.1142/S0219061314500020

M3 - Article

SN - 0219-0613

VL - 14

JO - Journal of Mathematical Logic

JF - Journal of Mathematical Logic

IS - 1

M1 - 1450002

ER -

Interpretable groups are definable

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this