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.
Bibliographical noteFunding 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
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