Zilber's conjecture for some o-minimal structures over the reals

Ya'acov Peterzil

doi:10.1016/0168-0072(93)90221-X

Zilber's conjecture for some o-minimal structures over the reals

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Abstract

We formulate an analogue of Zilber's conjecture for o-minimal structures in general, and then prove it for a class of o-minimal structures over the reals. We conclude in particular that if M is an ordered reduct of 〈R,<,+,·,e^x〉 whose theory T does not have the CF property then, given any model N of T, a real closed field is definable on a subinterval of N.

Original language	English
Pages (from-to)	223-239
Number of pages	17
Journal	Annals of Pure and Applied Logic
Volume	61
Issue number	3
DOIs	https://doi.org/10.1016/0168-0072(93)90221-X
State	Published - 11 Jun 1993
Externally published	Yes

ASJC Scopus subject areas

Logic

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10.1016/0168-0072(93)90221-X

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abstract = "We formulate an analogue of Zilber's conjecture for o-minimal structures in general, and then prove it for a class of o-minimal structures over the reals. We conclude in particular that if M is an ordered reduct of 〈R,<,+,·,ex〉 whose theory T does not have the CF property then, given any model N of T, a real closed field is definable on a subinterval of N.",

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AB - We formulate an analogue of Zilber's conjecture for o-minimal structures in general, and then prove it for a class of o-minimal structures over the reals. We conclude in particular that if M is an ordered reduct of 〈R,<,+,·,ex〉 whose theory T does not have the CF property then, given any model N of T, a real closed field is definable on a subinterval of N.

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M3 - Article

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JO - Annals of Pure and Applied Logic

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ER -

Zilber's conjecture for some o-minimal structures over the reals

Abstract

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