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The paper treats of some consequences of the model-theoretic version of Gabrielov's complement theorem from [11], which asserts that the theories T[sub an] (introduced in [11] and T'[sub an] (defined herein) are model-complete. The theory T'[sub an] is a universal modification of T[sub an] in the language L'[sub an] of ordered rings expanded by the symbols of restricted analytic functions, arithmetic roots and multiplicative inverse l/x. We give a short proof of the curve selecting lemma, and next we demonstrate how quantifier elimination, within the structure R[sub an] expanded by multiplicative inverse 1/x (a result due to Denef-van den Dries [4], can be obtained from the complement theorem through a general method of logic. Also presented is an application to definability problems ; namely, a piecewise description of a subanalytic function by restricted analytic functions, arithmetic roots and l/x.
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Rocznik
Tom
Strony
355--361
Opis fizyczny
Bibliogr. 14 poz.,
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- Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland
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Bibliografia
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bwmeta1.element.baztech-article-BAT2-0001-0941