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On Groups and Rings Definable In O–Minimal Expansions of Real Closed Fields
Author(s) -
Otero Margarita,
Peterzil Ya'acov,
Pillay Anand
Publication year - 1996
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/28.1.7
Subject(s) - mathematics , corollary , quaternion , ring (chemistry) , zero (linguistics) , field (mathematics) , pure mathematics , combinatorics , geometry , linguistics , chemistry , philosophy , organic chemistry
Let 〈 R , >,+,⋅〉 be a real closed field, and let M be an o‐minimal expansion of R . We prove here several results regarding rings and groups which are definable in M . We show that every M –definable ring without zero divisors is definably isomorphic to R , R (√(−l)) or the ring of quaternions over R . One corollary is that no model of T exp is interpretable in a model of T an .