Archive for Mathematical Logic

, Volume 52, Issue 7–8, pp 827–846 | Cite as

Strongly dominating sets of reals

  • Michal Dečo
  • Miroslav Repický


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.


Strongly dominating sets Laver perfect sets \({\kappa}\) -Suslin sets Laver category base Domination game 

Mathematics Subject Classification (2000)

Primary 03E15 Secondary 03E17 03E50 91A44 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Institute of MathematicsP. J. Šafárik UniversityKošiceSlovak Republic
  2. 2.Institute of MathematicsSlovak Academy of SciencesKošiceSlovak Republic

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