A model-theoretic criterion for quantifier elimination and its application to geometry

• Autorzy: Nowak K.
• Języki publikacji: EN

Abstrakty

EN

In this paper we present a model-theoretic criterion for quantifier elimination being a variant of Shoenfield's theorem (see [1], Chap. V, [paragraph]5). Our short proof is based directly on Godel's completeness and compactness theorems as well as on the concept of diagrams, and does not involve model-completeness or Robinson's test as does for instance the proof of certain related criteria given in [2], Chap. VIII, [paragraph]4. As a consequence, we immediately obtain the theorems of Chevalley and Tarski-Seidenberg from algebraic and semialalgebraic geometry.

Słowa kluczowe

EN

algebraically closed fields; diagrams; mathematical logic; model theory; quantifier elimination; real analytic geometry; real closed fields

PL

geometria algebraiczna; logika matematyczna; pole algebraicznie domknięte; pole rzeczywiste domknięte; teoria modeli

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 1998
• Tom: Vol. 46, no. 4
• Strony: 377--381
• Opis fizyczny: Bibliogr. 6 poz.,

Twórcy

autor

Nowak K.

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

Bibliografia

• [1] J. R. Shoenfield, Mathematical Logic, Addison-Wesley РиЫ. Co., Reading, Mass., 1967.
• [2] W. Hodges, Model Theory, Cambridge Univ. Press, 1993.
• [3] A. Тarski, A decision method for elementary algebra and geometry, Univ. California Press, Berkeley 1951 (2nd revised еd.).
• [4] J. Bochnak, M. Coste, M.-F. Roy, Géométrie. Algébrique Réelle, Springer-Verlag, 1987.
• [5] C. C. Chang, Н. J. Keisler, Model Theory, North-Holland Publ. Co., Amsterdam 1973.
• [6] K. J. Nowak, On a universal axiomnatization of the real closed fields, Ann. Polon. Math., 65(1) (1996) 95-103.