Cardinalities of 𝜂₁-ordered fields

Perović, Žikica

doi:10.1090/S0002-9939-1993-1132420-0

Cardinalities of $\eta _ 1$-ordered fields
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Proc. Amer. Math. Soc. 118 (1993), 379-384 Request permission

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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