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Strongly dominating sets of reals

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Abstract

We analyze the structure of strongly dominating sets of reals introduced in Goldstern et al. (Proc Am Math Soc 123(5):1573–1581, 1995). We prove that for every \({\kappa < \mathfrak{b}}\) a \({\kappa}\) -Suslin set \({A\subseteq{}^\omega\omega}\) is strongly dominating if and only if A has a Laver perfect subset. We also investigate the structure of the class l of Baire sets for the Laver category base and compare the σ-ideal of sets which are not strongly dominating with the Laver ideal l 0.

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Authors and Affiliations

  1. Institute of Mathematics, P. J. Šafárik University, Jesenná 5, 041 54, Košice, Slovak Republic

    Michal Dečo

  2. Institute of Mathematics, Slovak Academy of Sciences, Grešákova 6, 040 01, Košice, Slovak Republic

    Miroslav Repický

Authors
  1. Michal Dečo
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  2. Miroslav Repický
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Correspondence to Miroslav Repický.

Additional information

The first author was supported by grant VEGA 1/0002/12 and the second author was supported by grants VEGA 1/0002/12 and APVV-0269-11.

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Dečo, M., Repický, M. Strongly dominating sets of reals. Arch. Math. Logic 52, 827–846 (2013). https://doi.org/10.1007/s00153-013-0347-6

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  • DOI: https://doi.org/10.1007/s00153-013-0347-6

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