On groups and rings definable in o-minimal expansions of real closed fields

Margarita Otero; Ya'acov Peterzil; Anand Pillay

doi:10.1112/blms/28.1.7

On groups and rings definable in o-minimal expansions of real closed fields

Margarita Otero, Ya'acov Peterzil, Anand Pillay

Department of Mathematics

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

Abstract

Let 〈R, <, +, ·〉 be a real closed field, and let Script M sign be an o-minimal expansion of R. We prove here several results regarding rings and groups which are definable in Script M sign. We show that every Script M sign-definable ring without zero divisors is definably isomorphic to R, R(√(-1)) or the ring of quaternions over R. One corollary is that no model of T_exp is interpretable in a model of T_an.

Original language	English
Pages (from-to)	7-14
Number of pages	8
Journal	Bulletin of the London Mathematical Society
Volume	28
Issue number	1
DOIs	https://doi.org/10.1112/blms/28.1.7
State	Published - Jan 1996

Bibliographical note

Funding Information:
Received 25 May 1993; revised 12 January 1995. 1991 Mathematics Subject Classification 12L12. First author partially supported by a CICYT PB890379C0202 grant. Bull. London Math. Soc. 28 (1996) 7-14

ASJC Scopus subject areas

General Mathematics

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10.1112/blms/28.1.7

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abstract = "Let 〈R, <, +, ·〉 be a real closed field, and let Script M sign be an o-minimal expansion of R. We prove here several results regarding rings and groups which are definable in Script M sign. We show that every Script M sign-definable ring without zero divisors is definably isomorphic to R, R(√(-1)) or the ring of quaternions over R. One corollary is that no model of Texp is interpretable in a model of Tan.",

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AU - Pillay, Anand

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N2 - Let 〈R, <, +, ·〉 be a real closed field, and let Script M sign be an o-minimal expansion of R. We prove here several results regarding rings and groups which are definable in Script M sign. We show that every Script M sign-definable ring without zero divisors is definably isomorphic to R, R(√(-1)) or the ring of quaternions over R. One corollary is that no model of Texp is interpretable in a model of Tan.

AB - Let 〈R, <, +, ·〉 be a real closed field, and let Script M sign be an o-minimal expansion of R. We prove here several results regarding rings and groups which are definable in Script M sign. We show that every Script M sign-definable ring without zero divisors is definably isomorphic to R, R(√(-1)) or the ring of quaternions over R. One corollary is that no model of Texp is interpretable in a model of Tan.

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On groups and rings definable in o-minimal expansions of real closed fields

Abstract

Bibliographical note

ASJC Scopus subject areas

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