On cofinality of the smallest covering of the real line by meager sets II
We study the ideal of meager sets and related ideals.
math.LO↗
arXiv subjects
Tomek Bartoszynski
Publications and source records attributed to Tomek Bartoszynski.
Remarks on small sets related to trigonometric series
We show that several classes of sets, like N_0-sets, Arbault sets, N-sets and pseudo-Dirichlet sets are closed under adding sets of small size.
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Filters and games
We obtain game-theoretic characterizations for meagerness and rareness of filters on a countable set.
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Borel images of sets of reals
The main goal of this paper is to generalize several results concerning cardinal invariants to the statements about the associated families of sets. We also discuss the relationship between the additive properties of sets and their Borel images. Finally, we present estimates for the size of the smallest set which is not strongly meager.
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The Cichon diagram
We conclude the discussion of additivity, Baire number, uniformity and covering for measure and category by constructing the remaining 5 models. Thus we complete the analysis of Cichon's diagram.
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Closed measure zero sets
We study the relationship between the sigma-ideal generated by closed measure zero sets and the ideals of null and meager sets. We show that the additivity of the ideal of closed measure zero sets is not bigger than covering for category. As a consequence we get that the additivity of the ideal of closed measure zero sets is equal to the additivity of the ideal of meager sets.
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On the structure of measurable filters on a countable set
A combinatorial characterization of measurable filters on a countable set is found. We apply it to the problem of measurability of the intersection of nonmeasurable filters.
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Towards Martin's Minimum
We show that it is consistent with MA + the negation of CH, that the Forcing Axiom fails for all forcing notions in the class of omega^omega-bounding forcing notions with norms of "Norms on possibilities I: forcing with trees and creatures"(by Roslanowski and Shelah - math.LO/9807172).
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A note on duality between measure and category
A bijection from R to R is called an Erdos-Sierpinski mapping if it maps meager sets onto the first category sets and vice versa. We show that there is no Erdos-Sierpinski mapping preserving addition.
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Intersection of less than continuum ultrafilters may have measure zero
The goal of this paper is to prove the theorem in the title.
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Covering games and the Banach-Mazur game: k-tactics
Given a free ideal J of subsets of a set X, we consider games where player ONE plays an increasing sequence of elements of the sigma completion of J, and TWO tries to cover the union of this sequence by playing one set at a time from J. We describe various conditions under which player TWO has has a winning strategy that uses only information about the most recent k moves of ONE, and apply some of these results to the Banach-Mazur game.
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