# Ordered fields and the ultrafilter theorem

R. Berr; Françoise Delon; J. Schmid

Fundamenta Mathematicae (1999)

- Volume: 159, Issue: 3, page 231-241
- ISSN: 0016-2736

## Access Full Article

top## Abstract

top## How to cite

topBerr, R., Delon, Françoise, and Schmid, J.. "Ordered fields and the ultrafilter theorem." Fundamenta Mathematicae 159.3 (1999): 231-241. <http://eudml.org/doc/212331>.

@article{Berr1999,

abstract = {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.},

author = {Berr, R., Delon, Françoise, Schmid, J.},

journal = {Fundamenta Mathematicae},

keywords = {axiom of choice; formally real ring; semi-real; ordering; total preodering; ultrafilter theorem; JFM 52.0120.05; Artin-Schreier theorem},

language = {eng},

number = {3},

pages = {231-241},

title = {Ordered fields and the ultrafilter theorem},

url = {http://eudml.org/doc/212331},

volume = {159},

year = {1999},

}

TY - JOUR

AU - Berr, R.

AU - Delon, Françoise

AU - Schmid, J.

TI - Ordered fields and the ultrafilter theorem

JO - Fundamenta Mathematicae

PY - 1999

VL - 159

IS - 3

SP - 231

EP - 241

AB - 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.

LA - eng

KW - axiom of choice; formally real ring; semi-real; ordering; total preodering; ultrafilter theorem; JFM 52.0120.05; Artin-Schreier theorem

UR - http://eudml.org/doc/212331

ER -

## References

top- [1] E. Artin, Über die Zerlegung definiter Funktionen in Quadrate, Abh. Math. Sem. Univ. Hamburg 5 (1927), 100-115. Zbl52.0122.01
- [2] E. Artin, Schreier, O. Algebraische Konstruktion reeller Körper, ibid., 85-99.
- [3] T. Jech, The Axiom of Choice, North-Holland, 1973. Zbl0259.02051
- [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. Zbl0761.12004
- [6] A. Tarski, Prime ideal theorems for set algebras and ordering principles, preliminary report, Bull. Amer. Math. Soc. 60 (1954), 391.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.