An algebraic characterization of indistinguishable cardinals

Journal of Symbolic Logic 35 (1):97-104 (1970)
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Abstract

Two cardinals are said to beindistinguishableif there is no sentence of second order logic which discriminates between them. This notion, which is defined precisely below, is closely related to that ofcharacterizablecardinals, introduced and studied by Garland in [3]. In this paper we give an algebraic criterion for two cardinals to be indistinguishable. As a consequence we obtain a straightforward proof of an interesting theorem about characterizable cardinals due to Zykov [6].

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2009-01-28

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Alan Slomson
University of Leeds

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References found in this work

Introduction to mathematical logic.Alonso Church - 1958 - Revue de Métaphysique et de Morale 63 (1):118-118.
Models and Ultraproducts: An Introduction.J. L. Bell & A. B. Slomson - 1972 - Journal of Symbolic Logic 37 (4):763-764.

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