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The Journal of Symbolic Logic The Journal of Symbolic Logic

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A question of van den Dries and a theorem of Lipshitz and Robinson; Not everything is standard

Published online by Cambridge University Press:  12 March 2014

Ehud Hrushovski  and
Ya'acov Peterzil
Ehud Hrushovski
Affiliation:
Hebrew University, Department of Mathematics, Jerusalem, Israel. E-mail: ehud@math.huji.ac.il
Ya'acov Peterzil
Affiliation:
University of Haifa, Department of Mathematics, Haifa, Israel. E-mail: kobi@math.haifa.ac.il
Corresponding
E-mail address:
ehud@math.huji.ac.il
kobi@math.haifa.ac.il
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Abstract

We use a new construction of an o-minimal structure, due to Lipshitz and Robinson, to answer a question of van den Dries regarding the relationship between arbitrary o-minimal expansions of real closed fields and structures over the real numbers. We write a first order sentence which is true in the Lipshitz-Robinson structure but fails in any possible interpretation over the field of real numbers.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 72 , Issue 1 , March 2007 , pp. 119 - 122
Copyright
Copyright © Association for Symbolic Logic 2007

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References

[1]Berarducci, A. and Servi, T., An effective version of Wilkie's theorem of the complement and some effective o-minimality results, Annals of Pure and Applied Logic, vol. 125 (2004), no. 1–3, pp. 43–74.CrossRefGoogle Scholar
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[4]Lipshitz, L. and Robinson, Z., Overconvergent real closed quantifier elimination, Bulletin of the London Mathematical Society, to appear.Google Scholar
[5]Peterzil, Y. and Starchenko, S., A trichotomy theorem for o-minimal structures, Proceedings of the London Mathematical Society (3), vol. 77 (1998), no. 3, pp. 481–523.CrossRefGoogle Scholar
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