On a universal axiomatization of the real closed fields

Krzysztof Jan Nowak

Annales Polonici Mathematici (1996)

  • Volume: 65, Issue: 1, page 95-103
  • ISSN: 0066-2216

Abstract

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

How to cite

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Krzysztof Jan Nowak. "On a universal axiomatization of the real closed fields." Annales Polonici Mathematici 65.1 (1996): 95-103. <http://eudml.org/doc/270007>.

@article{KrzysztofJanNowak1996,
abstract = {This paper presents a natural axiomatization of the real closed fields. It is universal and admits quantifier elimination.},
author = {Krzysztof Jan Nowak},
journal = {Annales Polonici Mathematici},
keywords = {real closed fields; real valuations; Nash functions; quantifier elimination; axiomatization},
language = {eng},
number = {1},
pages = {95-103},
title = {On a universal axiomatization of the real closed fields},
url = {http://eudml.org/doc/270007},
volume = {65},
year = {1996},
}

TY - JOUR
AU - Krzysztof Jan Nowak
TI - On a universal axiomatization of the real closed fields
JO - Annales Polonici Mathematici
PY - 1996
VL - 65
IS - 1
SP - 95
EP - 103
AB - This paper presents a natural axiomatization of the real closed fields. It is universal and admits quantifier elimination.
LA - eng
KW - real closed fields; real valuations; Nash functions; quantifier elimination; axiomatization
UR - http://eudml.org/doc/270007
ER -

References

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  1. [1] Artin, E., Schreier, O.: Algebraische Konstruktion reeller Körper, Abh. Math. Sem. Univ. Hamburg 5 (1927), 85-99. 
  2. [2] Bierstone, E., Milman, P. D.: Semianalytic and subanalytic sets, Publ. Math. I.H.E.S. 67 (1988), 1-42. Zbl0674.32002
  3. [3] Bochnak, J., Coste, M., Roy, M.-F.: Géométrie Algébrique Réelle, Springer, 1987. 
  4. [4] Chang, C. C., Keisler, H. J.: Model Theory, North-Holland, Amsterdam, 1973. 
  5. [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. Zbl0435.32006
  6. [6] Keisler, H. J.: Fundamentals of model theory, in: Handbook of Mathematical Logic, North-Holland, Amsterdam, 1977, 47-103. 
  7. [7] Łoś, J.: On the extending of models I, Fund. Math. 42 (1955), 38-54. Zbl0065.00401
  8. [8] Prestel, A.: Lectures on Formally Real Fields, Lecture Notes in Math. 1093, Springer, 1984. Zbl0548.12011
  9. [9] Ribbenboim, P.: Théorie des Valuations, Les Presses de l'Université de Montréal, 1968. 
  10. [10] Tarski, A.: The Completeness of Elementary Algebra and Geometry, Hermann, Paris, 1940. 
  11. [11] Tarski, A.: Contributions to the theory of models I, II, Indag. Math. 16 (1954), 572-588. Zbl0058.24702

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