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The γ-borel conjecture

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Abstract.

In this paper we prove that it is consistent that every γ-set is countable while not every strong measure zero set is countable. We also show that it is consistent that every strong γ-set is countable while not every γ-set is countable. On the other hand we show that every strong measure zero set is countable iff every set with the Rothberger property is countable.

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Authors and Affiliations

  1. Department of Mathematics, University of Wisconsin-Madison, Van Vleck Hall, 480 Lincoln Drive, Madison, Wisconsin, 53706-1388, USA

    Arnold W. Miller

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  1. Arnold W. Miller
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Correspondence to Arnold W. Miller.

Additional information

Thanks to Boise State University for support during the time this paper was written and to Alan Dow for some helpful discussions and to Boaz Tsaban for some suggestions to improve an earlier version.

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Miller, A. The γ-borel conjecture. Arch. Math. Logic 44, 425–434 (2005). https://doi.org/10.1007/s00153-004-0260-0

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  • DOI: https://doi.org/10.1007/s00153-004-0260-0

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