A model-theoretic version of the complement theorem : applications

• Autorzy: Nowak K.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

first-order logic; model-completeness; quantifier elimination; real analytic functions; real valuations; subanalytic functions; subanalytic sets

PL

eliminacja kwantyfikatorów; funkcja rzeczywista analityczna; funkcje zmiennych zespolonych; logika pierwszego rzędu; model uzupełnień; przestrzeń analityczna

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 1999
• Tom: Vol. 47, no 4
• Strony: 355--361
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Nowak K.

• Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

Bibliografia

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• [11] K. J. Nowak, A model-theoretic version of the complement theorem, Bull. Pol. Ac.: Math., 47 (4) (1999), 345-353.
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