Strongly dominating sets of reals

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 $${\kappa < \mathfrak{b}}$$ ? < b a $${\kappa}$$ ? -Suslin set $${A\subseteq{}^\omega\omega}$$ A ⊆ ? ? 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 ?-ideal of sets which are not strongly dominating with the Laver ideal l 0.