Archive for Mathematical Logic 52 (7-8):827-846 (2013)

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
Keywords Strongly dominating sets  Laver perfect sets   $${\kappa}$$ κ -Suslin sets  Laver category base  Domination game
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DOI 10.1007/s00153-013-0347-6
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References found in this work BETA

Isolating Cardinal Invariants.Jindřich Zapletal - 2003 - Journal of Mathematical Logic 3 (1):143-162.
Sacks Forcing, Laver Forcing, and Martin's Axiom.Haim Judah, Arnold W. Miller & Saharon Shelah - 1992 - Archive for Mathematical Logic 31 (3):145-161.
Regularity Properties for Dominating Projective Sets.Jörg Brendle, Greg Hjorth & Otmar Spinas - 1995 - Annals of Pure and Applied Logic 72 (3):291-307.
Dominating Projective Sets in the Baire Space.Otmar Spinas - 1994 - Annals of Pure and Applied Logic 68 (3):327-342.

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Citations of this work BETA

Strongly Unbounded and Strongly Dominating Sets of Reals Generalized.Michal Dečo - 2015 - Archive for Mathematical Logic 54 (7-8):825-838.

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