3 citations · 3 across the 3 of their papers we have counts for
15 papers · 1 filter
Invariants of Measure and Category
Tomek Bartoszynski
A survey of recent results concerning cardinal invariants of measure and category. Submitted as a chapter of the upcoming Handbook of Set Theory.
Strongly meager and strong measure zero sets
Tomek Bartoszynski, Saharon Shelah
We show that the following are consistent with ZFC: 1. Strongly meager sets form an ideal with the same additivity as the ideal of meager sets. 2. There exists a strong measure zer…
On the structure of measurable filters on a countable set
Tomek Bartoszynski
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.
Closed measure zero sets
Tomek Bartoszynski, Saharon Shelah
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 m…
The Cichon diagram
Tomek Bartoszynski, Haim Judah, Saharon Shelah
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 Ci…
A-sets
Tomek Bartoszynski, Marion Scheepers
We consider ``meager analogues'' of classical covering properties of Menger, Hurewicz and Rothberger. We show that Borel images of sets having ``our'' covering properties have thes…