On a universal axiomatization of the real closed fields

• Autorzy: Krzysztof Jan Nowak
• Języki publikacji: EN

Abstrakty

EN

This paper presents a natural axiomatization of the real closed fields. It is universal and admits quantifier elimination.

Słowa kluczowe

EN

real closed fields   real valuations   Nash functions   quantifier elimination  

Kategorie tematyczne

• 12D15: Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
• 03C10: Quantifier elimination, model completeness and related topics
• 14P20: Nash functions and manifolds

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1996-1997
• Tom: 65
• Numer: 1
• Strony: 95-103

Daty

wydano

1996

otrzymano

1996-01-08

Twórcy

autor

Krzysztof Jan Nowak

• Faculteit der Wiskunde en Informatica, Vrije Universiteit, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands
• Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

Bibliografia

• [1] Artin, E., Schreier, O.: Algebraische Konstruktion reeller Körper, Abh. Math. Sem. Univ. Hamburg 5 (1927), 85-99.
• [2] Bierstone, E., Milman, P. D.: Semianalytic and subanalytic sets, Publ. Math. I.H.E.S. 67 (1988), 1-42.
• [3] Bochnak, J., Coste, M., Roy, M.-F.: Géométrie Algébrique Réelle, Springer, 1987.
• [4] Chang, C. C., Keisler, H. J.: Model Theory, North-Holland, Amsterdam, 1973.
• [5] m Denkowska, Z., Łojasiewicz, S., Stasica, J.: Certaines propriétés élémentaires des ensembles sous-analytiques, Bull. Acad. Polon. Sci. Sér. Sci. Math. 27 (1979), 529-536.
• [6] Keisler, H. J.: Fundamentals of model theory, in: Handbook of Mathematical Logic, North-Holland, Amsterdam, 1977, 47-103.
• [7] Łoś, J.: On the extending of models I, Fund. Math. 42 (1955), 38-54.
• [8] Prestel, A.: Lectures on Formally Real Fields, Lecture Notes in Math. 1093, Springer, 1984.
• [9] Ribbenboim, P.: Théorie des Valuations, Les Presses de l'Université de Montréal, 1968.
• [10] Tarski, A.: The Completeness of Elementary Algebra and Geometry, Hermann, Paris, 1940.
• [11] Tarski, A.: Contributions to the theory of models I, II, Indag. Math. 16 (1954), 572-588.