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Goldstern–Judah–Shelah preservation theorem for countable support iterations

Miroslav Repický — 1994

Fundamenta Mathematicae

[1] T. Bartoszyński, Additivity of measure implies additivity of category, Trans. Amer. Math. Soc. 281 (1984), 209-213. [2] T. Bartoszyński and H. Judah, Measure and Category, in preparation. [3] D. H. Fremlin, Cichoń’s diagram, Publ. Math. Univ. Pierre Marie Curie 66, Sém. Initiation Anal., 1983/84, Exp. 5, 13 pp. [4] M. Goldstern, Tools for your forcing construction, in: Set Theory of the Reals, Conference of Bar-Ilan University, H. Judah (ed.), Israel Math. Conf. Proc. 6, 1992, 307-362. [5] H....

Perfect sets and collapsing continuum

Miroslav Repický — 2003

Commentationes Mathematicae Universitatis Carolinae

Under Martin’s axiom, collapsing of the continuum by Sacks forcing 𝕊 is characterized by the additivity of Marczewski’s ideal (see [4]). We show that the same characterization holds true if 𝔡 = 𝔠 proving that under this hypothesis there are no small uncountable maximal antichains in 𝕊 . We also construct a partition of ω 2 into 𝔠 perfect sets which is a maximal antichain in 𝕊 and show that s 0 -sets are exactly (subsets of) selectors of maximal antichains of perfect sets.

Spaces not distinguishing convergences

Miroslav Repický — 2000

Commentationes Mathematicae Universitatis Carolinae

In the present paper we introduce a convergence condition ( Σ ' ) and continue the study of “not distinguish” for various kinds of convergence of sequences of real functions on a topological space started in [2] and [3]. We compute cardinal invariants associated with introduced properties of spaces.

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