3 citations · 3 across the 3 of their papers we have counts for
24 papers
There may be no Hausdorff ultrafilters
Tomek Bartoszynski, Saharon Shelah
An ultrafilter U is Hausdorff if for any two functions f,g mapping N to N, f(U)=g(U) iff f(n)=g(n) for n in some X in U. We will show that it is consistent that there are no Hausdo…
Strongly meager sets of size continuum
Tomek Bartoszynski, Saharon Shelah
We construct several models where there are no strongly meager sets of size continuum. In particular, there are no such sets in the Laver's model.
Hechler's theorem for the meager ideal
Tomek Bartoszynski, Masaru Kada
We prove the following theorem: For a partially ordered set Q such that every countable subset has a strict upper bound, there is a forcing notion satisfying ccc such that, in the…
Strongly meager sets can be quite big
Tomek Bartoszynski, Andrzej Nowik, Tomasz Weiss
The paper contains two results pointing to the lack of symmetry between measure and category. Assume CH. There exists a strongly meager subset of the Cantor set that can be mapped…
Remarks on small sets of reals
Tomek Bartoszynski
We show that the Dual Borel Conjecture implies that and find some topological characterizations of perfectly meager and universally meager sets.
On a theorem of Banach and Kuratowski and K-Lusin sets
Tomek Bartoszynski, Lorenz Halbeisen
In a paper of 1929, Banach and Kuratowski proved, assuming the continuum hypothesis, a combinatorial theorem which implies that there is no non-vanishing sigma-additive finite meas…