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On sets ∀-definable from Pfaffian functions

Published online by Cambridge University Press:  12 March 2014

Ricardo Bianconi*
Affiliation:
Instituto de Matematica e Estatistica, Universidade De São Paulo, 01498 São Paulo, Brazil, E-mail: bianconi@ime.usp.br

Abstract

We prove the existence of a bound to the number of components of an ∀-definable set in the reals, using Pfaffian functions, and give some applications.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1992

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References

[Bia]Bianconi, R., Some results in the model theory of analytic functions, doctoral thesis, University of Oxford, Oxford, 1990.Google Scholar
[Kho1]Khovanskiǐ, A. G., On a class of systems of transcendental equations, Soviet Mathematics Doklady, vol. 22 (1980), pp. 762765.Google Scholar
[Kho2]Khovanskiǐ, A. G., Real analytic varieties with the finiteness property and complex abelian integrals, Functional Analysis and its Applications, vol. 14 (1984), pp. 119127.CrossRefGoogle Scholar
[Mas]Massey, W. S., Singular homology theory, Springer-Verlag, New York, 1980.CrossRefGoogle Scholar
[Wil]Wilkie, A. J., Some model theory for Pfaffian functions, manuscript, Oxford, 1987.Google Scholar

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On sets ∀-definable from Pfaffian functions
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