EUDML

Currently displaying 1 – 10 of 10

Order by Relevance | Title | Year of publication

Spaces not distinguishing convergences.

Repický, Miroslav — 2000

Commentationes Mathematicae Universitatis Carolinae

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....

Properties of forcing preserved by finite support iterations

Miroslav Repický — 1991

Commentationes Mathematicae Universitatis Carolinae

We shall investigate some properties of forcing which are preserved by finite support iterations and which ensure that unbounded families in given partially ordered sets remain unbounded.

Permitted trigonometric thin sets and infinite combinatorics

Miroslav Repický — 2001

Commentationes Mathematicae Universitatis Carolinae

We investigate properties of permitted trigonometric thin sets and construct uncountable permitted sets under some set-theoretical assumptions.

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.

A proof of the independence of the Axiom of Choice from the Boolean Prime Ideal Theorem

Miroslav Repický — 2015

Commentationes Mathematicae Universitatis Carolinae

We present a proof of the Boolean Prime Ideal Theorem in a transitive model of ZF in which the Axiom of Choice does not hold. We omit the argument based on the full Halpern-Läuchli partition theorem and instead we reduce the proof to its elementary case.

Cohen real and disjoint refinement of perfect sets

Miroslav Repický — 2000

Commentationes Mathematicae Universitatis Carolinae

We prove that if there exists a Cohen real over a model, then the family of perfect sets coded in the model has a disjoint refinement by 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.