On Groups and Rings Definable In O–Minimal Expansions of Real Closed Fields | Zendy

Otero Margarita | Zendy; Peterzil Ya'acov | Zendy; Pillay Anand | Zendy

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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 .

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