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Models of Peano Arithmetic and a question of Sikorski on ordered fields

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Abstract

Using models of Peano Arithmetic, we solve a problem of Sikorski by showing that the existence of an ordered field of cardinalityλ with the Bolzano-Weierstrass property forκ-sequences is equivalent to the existence of aκ-tree with exactlyλ branches and with noκ-Aronszajn subtrees.

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Authors and Affiliations

  1. Department of Mathematics, University of Connecticut, 06268, Storrs, CT, USA

    James H. Schmerl

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  1. James H. Schmerl
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Supported in part by NSF Grant MCS-8301603.

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Schmerl, J.H. Models of Peano Arithmetic and a question of Sikorski on ordered fields. Israel J. Math. 50, 145–159 (1985). https://doi.org/10.1007/BF02761121

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  • DOI: https://doi.org/10.1007/BF02761121

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