Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-26T12:53:24.335Z Has data issue: false hasContentIssue false

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: [email protected]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

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