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