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Uniform model-completeness for the real field expanded by power functions

Published online by Cambridge University Press:  12 March 2014

Tom Foster
Tom Foster*
Affiliation:
Mathematical Institute, University of Oxford, 24-29 ST GILES', Oxford, Ox1 3LB, UK. E-mail: fostert@maths.ox.ac.uk
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Abstract

We prove that given any first order formula ϕ in the language L′ = {+, ·, <,(fi)iЄI, (ci)iЄI}, where the fi are unary function symbols and the ci are constants, one can find an existential formula Ψ such that φ and Ψ are equivalent in any L′-structure

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 75 , Issue 4 , December 2010 , pp. 1441 - 1461
Copyright
Copyright © Association for Symbolic Logic 2010

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References

REFERENCES

[1]Jones, G. O. and Wilkie, A. J., Locally polynomially bounded structures, Bulletin of the London Mathematical Society, vol. 40 (2008), no. 2, pp. 239–248.CrossRefGoogle Scholar
[2]Miller, Chris, Expansions of the realfield with power functions, Annals of Pure and Applied Logic, vol. 68 (1994), no. 1, pp. 79–94.CrossRefGoogle Scholar
[3]Miller, Chris, Exponentiation is hard to avoid, Proceedings of the American Mathematical Society, vol. 122 (1994), no. 1, pp. 257–259.CrossRefGoogle Scholar
[4]Miller, Chris, A growth dichotomy for o-minimal expansions of ordered fields, Logic: from foundations to applications (Staffordshire, 1993), Oxford Scientific Publications, Oxford University Press, New York, 1996, pp. 385–399.CrossRefGoogle Scholar
[5]Sacks, G. E., Saturated model theory, W. A. Benjamin, Inc., 1972.Google Scholar
[6]van den Dries, Lou, A generalization of the Tarski–Seidenberg theorem, and some nondefinability results, American Mathematical Society. Bulletin. New Series, vol. 15 (1986), no. 2, pp. 189–193.CrossRefGoogle Scholar
[7]van den Dries, Lou, T-convexity and tame extensions. II, this Journal, vol. 62 (1997), no. 1, pp. 14–34.Google Scholar
[8]van den Dries, Lou, Tame topology and o-minimal structures, London Mathematical Society Lecture Note Series, vol. 248, Cambridge University Press, Cambridge, 1998.CrossRefGoogle Scholar
[9]van den Dries, Lou and Lewenberg, Adam H., T-convexity and tame extensions, this Journal, vol. 60 (1995), no. 1, pp. 74–102.Google Scholar
[10]Wilkie, A. J., Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function, Journal of the American Mathematical Society, vol. 9 (1996), no. 4, pp. 1051–1094.CrossRefGoogle Scholar