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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Cardinalities of $ \eta\sb 1$-ordered fields


Author: Žikica Perović
Journal: Proc. Amer. Math. Soc. 118 (1993), 379-384
MSC: Primary 12J15; Secondary 03E05, 03E75, 04A30, 12L99
MathSciNet review: 1132420
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Abstract: We show, using GCH, that a cardinal $ \kappa $ is the cardinality of an $ {\eta _1}$-ordered field iff $ {\kappa ^\omega } = \kappa $. We also show, without using GCH, that a cardinal $ \kappa $ is the cardinality of a maximally valued $ {\eta _1}$-ordered field only if $ {\kappa ^\omega } = \kappa $.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1132420-0
PII: S 0002-9939(1993)1132420-0
Article copyright: © Copyright 1993 American Mathematical Society