Ordered fields and the ultrafilter theorem

• Autorzy: R. Berr , Françoise Delon , J. Schmid
• Języki publikacji: EN

Abstrakty

EN

We prove that on the basis of ZF the ultrafilter theorem and the theorem of Artin-Schreier are equivalent. The latter says that every formally real field admits a total order.

Kategorie tematyczne

• 12J15: Ordered fields

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1999
• Tom: 159
• Numer: 3
• Strony: 231-241

Daty

wydano

1999

otrzymano

1998-03-03

poprawiono

1998-05-05

Twórcy

autor

R. Berr

• Fachbereich Mathematik, Universität Dortmund, D-44221 Dortmund, Germany

autor

Françoise Delon

• CNRS-UFR de Mathématiques, Université Paris 7, 2 Place Jussieu, Case 7012, F-75251 Paris Cedex 05, France

autor

J. Schmid

• Fachbereich Mathematik, Universität Dortmund, D-44221 Dortmund, Germany

Bibliografia

• [1] E. Artin, Über die Zerlegung definiter Funktionen in Quadrate, Abh. Math. Sem. Univ. Hamburg 5 (1927), 100-115.
• [2] E. Artin, Schreier, O. Algebraische Konstruktion reeller Körper, ibid., 85-99.
• [3] T. Jech, The Axiom of Choice, North-Holland, 1973.
• [4] H. Lombardi and M.-F. Roy, Constructive elementary theory of ordered fields, in: Effective Methods in Algebraic Geometry, Progr. Math. 94, Birkhäuser, 1991, 249-262.
• [5] T. Sander, Existence and uniqueness of the real closure of an ordered field without Zorn's Lemma, J. Pure Appl. Algebra 73 (1991), 165-180.
• [6] A. Tarski, Prime ideal theorems for set algebras and ordering principles, preliminary report, Bull. Amer. Math. Soc. 60 (1954), 391.