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  1. Amoeba Reals.Haim Judah & Miroslav Repickẏ - 1995 - Journal of Symbolic Logic 60 (4):1168-1185.
    We define the ideal with the property that a real omits all Borel sets in the ideal which are coded in a transitive model if and only if it is an amoeba real over this model. We investigate some other properties of this ideal. Strolling through the "amoeba forest" we gain as an application a modification of the proof of the inequality between the additivities of Lebesgue measure and Baire category.
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  2.  10
    Strongly Dominating Sets of Reals.Michal Dečo & Miroslav Repický - 2013 - Archive for Mathematical Logic 52 (7-8):827-846.
    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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  3.  26
    Hechler Reals.Grzegorz Łabędzki & Miroslav Repický - 1995 - Journal of Symbolic Logic 60 (2):444-458.
    We define a σ-ideal J D on the set of functions ω ω with the property that a real x ∈ ω ω is a Hechler real over V if and only if x omits all Borel sets in J D . In fact we define a topology D on ω ω related to Hechler forcing such that J D is the family of first category sets in D. We study cardinal invariants of the ideal J D.
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  4.  20
    Cardinal Invariants and the Collapse of the Continuum by Sacks Forcing.Miroslav Repický - 2008 - Journal of Symbolic Logic 73 (2):711 - 727.
    We study cardinal invariants of systems of meager hereditary families of subsets of ω connected with the collapse of the continuum by Sacks forcing S and we obtain a cardinal invariant yω such that S collapses the continuum to yω and y ≤ yω ≤ b. Applying the Baumgartner-Dordal theorem on preservation of eventually narrow sequences we obtain the consistency of y = yω < b. We define two relations $\leq _{0}^{\ast}$ and $\leq _{1}^{\ast}$ on the set $(^{\omega}\omega)_{{\rm Fin}}$ of (...)
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    Sets of Points of Symmetric Continuity.Miroslav Repický - 2015 - Archive for Mathematical Logic 54 (7-8):803-824.
    We study the sets of symmetric continuity of real functions in connection with the sets of continuity. We prove that sets of reals of cardinality (...)
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