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Lindelöf models of the reals: Solution to a problem of Sikorski

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Abstract

We show that it is consistent with ZFC that there is a modelM of ZF + DC such that the integers ofM areω 1-like, the reals ofM have cardinalityω 2, and the unit interval [0, 1]M is Lindelöf (i.e. every open cover has a countable subcover). This answers an old question of Sikorski.

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Authors and Affiliations

  1. Department of Mathematics, Bar Ilan University, Ramat Gan, Israel

    Larry Manevitz & Arnold W. Miller

  2. Department of Mathematics, The University of Texas, 78712, Austin, TX, USA

    Larry Manevitz & Arnold W. Miller

Authors
  1. Larry Manevitz
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  2. Arnold W. Miller
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Partially supported by a Binational Science Foundation Grant.

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Manevitz, L., Miller, A.W. Lindelöf models of the reals: Solution to a problem of Sikorski. Israel J. Math. 45, 209–218 (1983). https://doi.org/10.1007/BF02774017

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  • DOI: https://doi.org/10.1007/BF02774017

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