Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6826(e) ISSN 0002-9939(p)

Metrizable and $\mathbb R$ -metrizable betweenness spaces

Author(s): Juraj Simko
Journal: Proc. Amer. Math. Soc. 127 (1999), 323-325.
MSC (1991): Primary 03B30, 03C52, 51F99
MathSciNet review: 1458264
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: It is proved that the theory of the class of all betweenness spaces metrizable by real-valued metrics does not coincide with the theory of the class of all betweenness spaces metrizable by metrics taking values in any ordered field. This solves a problem raised by Mendris and Zlato\v{s}.

References:

[1]: R. Mendris and P. Zlato\v{s}, Axiomatization and undecidability results for metrizable betweenness relations, Proc. Amer. Math. Soc. 123 (1995), 873-882. MR 95d:03008

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 03B30, 03C52, 51F99

Retrieve articles in all Journals with MSC (1991): 03B30, 03C52, 51F99

Additional Information:

Juraj Simko
Affiliation: Department of Mathematics, Faculty of Chemical Technology, Slovak Technical University, 81237~Bratislava, Slovakia
Email: simko@cvt.stuba.sk

DOI: 10.1090/S0002-9939-99-04515-3
PII: S 0002-9939(99)04515-3
Keywords: Betweenness relation, metric, ordered field, elementary class
Received by editor(s): April 2, 1997
Received by editor(s) in revised form: May 15, 1997
Communicated by: Carl G. Jockusch, Jr.
Copyright of article: Copyright 1999, American Mathematical Society

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|