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On the Number of Sets Definable by Polynomials

✍ Scribed by Gabriela Jeronimo; Juan Sabia

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
102 KB
Volume
227
Category
Article
ISSN
0021-8693

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✦ Synopsis

We show that the known algorithms used to re-write any first order quantifierfree formula over an algebraically closed field into its normal disjunctive form are essentially optimal. This result follows from an estimate of the number of sets definable by equalities and inequalities of fixed polynomials. Finally we apply our results to obtain similar estimates in the real case.

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