A model-theoretic version of the complement theorem

• Autorzy: Nowak K.
• Języki publikacji: EN

Abstrakty

EN

This paper deals with an axiomatic theory T[sub an] and the expansion R[sub an] of the ordered field of reals, formed by attaching the restricted analytic functions. We show that the theory T[sub an] is model-complete, which may be regarded as a version of Gabrielov's complement theorem. Our proof is based on Robinson's test and it does not involve a partition technique. An immediate corollary is that T[sub an] coincides with the semantic theory Th(R[sub an]) of all sentences true in the structure R[sub an].

Słowa kluczowe

EN

first-order logic; model-completeness; real analytic functions; Robinson's test; semianalytic sets; subanalytic sets

PL

funkcja rzeczywista analityczna; funkcje wielu zmiennych zespolonych; logika pierwszego rzędu; model uzupełnień; przestrzeń analityczna; semianalityczny zbiór; subanalityczny zbiór; test Robinsona

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 1999
• Tom: Vol. 47, no 4
• Strony: 345--353
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Nowak K.

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

Bibliografia

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• [10] K. J. Nowak, A model-theoretic version of the complement theorem: Applications, Bull. Pol. Ac.: Math., 47 (4) (1999), 355-361.
• [11] A. Robinson, Complete Theories, North-Holland Publ. Co., Amsterdam 1956.
• [12] A. Tarski, A decision method for elementary algebra and geometry, Univ. California Press, Berkeley 1951 (2nd revised ed.).