OCA and towers in
We shall show that Open Coloring Axiom has different influence on the algebra than on . The tool used to accomplish this is forcing with a Suslin tree.
On a certain prewellordering
On a classification of denumerable order types and an application to the partition calculus
On a paper by Karel Prikry concerning Ulam's problem on families of measures
On a problem of Steve Kalikow
The Kalikow problem for a pair (λ,κ) of cardinal numbers,λ > κ (in particular κ = 2) is whether we can map the family of ω-sequences from λ to the family of ω-sequences from κ in a very continuous manner. Namely, we demand that for η,ν ∈ ω we have: η, ν are almost equal if and only if their images are. We show consistency of the negative answer, e.g., for but we prove it for smaller cardinals. We indicate a close connection with the free subset property and its variants.
On a sharp estimation in the theory of binary relations on a finite set
On a theorem of Baumgartner and Weese
On absolutely divergent series
We show that in the -stage countable support iteration of Mathias forcing over a model of CH the complete Boolean algebra generated by absolutely divergent series under eventual dominance is not isomorphic to the completion of P(ω)/fin. This complements Vojtáš’ result that under the two algebras are isomorphic [15].
On an extremal characterization of partitions
On automorphisms of Boolean algebras embedded in P (ω)/fin
We prove that, under CH, for each Boolean algebra A of cardinality at most the continuum there is an embedding of A into P(ω)/fin such that each automorphism of A can be extended to an automorphism of P(ω)/fin. We also describe a model of ZFC + MA(σ-linked) in which the continuum is arbitrarily large and the above assertion holds true.
On axial maps of direct product,s I
On axial maps of direct products, II
On CCC boolean algebras and partial orders
We partially strengthen a result of Shelah from [Sh] by proving that if and is a CCC partial order with e.g. (the successor of ) and then is -linked.
On characteristic sets of a system of equivalence relations
On chromatic number of product of graphs
On Ciesielski's problems.
On club-like principles on regular cardinals above
On collections of almost disjoint families
On dense subsets of rational numbers
On diamond sequences