A 2-coloring of can have monochromatic Schur triples, but not less.
A Čech function in ZFC
A nontrivial surjective Čech closure function is constructed in ZFC.
A characterization of determinacy for Turing degree games
A consistency result on weak reflection
A deceptive fact about functions
The paper provides a proof of a combinatorial result which pertains to the characterization of the set of equations which are solvable in the composition monoid of all partial functions on an infinite set.
A dichotomy for P-ideals of countable sets
A dichotomy concerning ideals of countable subsets of some set is introduced and proved compatible with the Continuum Hypothesis. The dichotomy has influence not only on the Suslin Hypothesis or the structure of Hausdorff gaps in the quotient algebra / but also on some higher order statements like for example the existence of Jensen square sequences.
A fine hierarchy of partition cardinals
A free group of piecewise linear transformations
We prove the following conjecture of J. Mycielski: There exists a free nonabelian group of piecewise linear, orientation and area preserving transformations which acts on the punctured disk {(x,y) ∈ ℝ²: 0 < x² + y² < 1} without fixed points.
A new construction of a Kurepa tree with no Aronszajn subtree
A non-special -tree with special -subtrees
A note on a question of Abe
Assuming large cardinals, we show that every κ-complete filter can be generically extended to a V-ultrafilter with well-founded ultrapower. We then apply this to answer a question of Abe.
A note on almost disjoint refinement
A note on automorphisms and partitions
A note on Boolean algebras
We show that splitting of elements of an independent family of infinite regular size will produce a full size independent set.
A note on forcing with ideals and Hechler forcing
A note on nowhere dense sets in
A note on the intersection ideal
We prove among other theorems that it is consistent with that there exists a set which is not meager additive, yet it satisfies the following property: for each measure zero set , belongs to the intersection ideal .
A note on the Ramsey-type theorem of Erdös
A note on the structure of WUR Banach spaces
We present an example of a Banach space admitting an equivalent weakly uniformly rotund norm and such that there is no , for any set , linear, one-to-one and bounded. This answers a problem posed by Fabian, Godefroy, Hájek and Zizler. The space is actually the dual space of a space which is a subspace of a WCG space.
A note on the λ-Shelah property