10 citations · 12 across the 5 of their papers we have counts for
7 papers
The linear refinement number and selection theory
Michał Machura, Saharon Shelah, Boaz Tsaban
The \emph{linear refinement number} is the minimal cardinality of a centered family in such that no linearly ordered set in refines th…
On critical cardinalities related to -sets
Taras Banakh, Michal Machura, Lubomyr Zdomskyy
In this note we collect some known information and prove new results about the small uncountable cardinal . The cardinal is defined as the smallest c…
Thin ultrafilters, P-hierarchu and MArtin Axiom
Michał Machura, Andrzej Starosolski
Under MA we prove that for the ideal of thin sets on and for any ordinal there is an -ultrafilter (in the sense of Baumgartner), which belongs to…
How high can Baumgartner's {\cal I}-ultrafilters lie in the P-hierarchy?
Michał Machura, Andrzej Starosolski
Under CH we prove that for any tall ideal on and for any ordinal there is an -ultrafilter (in the sense of Baumgartner), which belongs to the cla…
Spaces of - places of rational function fields
Michał Machura, Katarzyna Osiak
In the paper an answer to a problem "When different orders of R(X) (where R is a real closed field) lead to the same real place ?" is given. We use this result to show that the spa…
Squares of Menger-bounded groups
Michal Machura, Saharon Shelah, Boaz Tsaban
Using the Continuum Hyporthesis, we prove that there is a Menger-bounded (also called o-bounded) subgroup of the Baer-Specker group Z^N, whose square is not Menger-bounded. This se…