DTC ultrafilters on groups

Ultrafilters and Abelian Groups

ON SOFT ULTRAFILTERS

In this paper, the concept of soft ultrafilters is introduced and some of the related structures such as soft Stone-Cech compactification, principal soft ultrafilters and basis for its topology are studied.

Nonregular ultrafilters on ω2

We obtain lower bounds for the consistency strength of fully nonregular ultrafilters on ω2.

On Milliken-Taylor Ultrafilters

We show that there may be a Milliken-Taylor ultrafilter with infinitely many near coherence classes of ultrafilters in its projection to ω, answering a question by López-Abad. We show that k-coloured Milliken-Taylor ultrafilters have at least k + 1 near coherence classes of ultrafilters in its projection to ω. We show that the Mathias forcing with a Milliken-Taylor ultrafilter destroys all Mill...

Ultrafilters and Partial Products of Infinite Cyclic Groups

We consider, for infinite cardinals κ and α ≤ κ+, the group Π(κ,<α) of sequences of integers, of length κ, with non-zero entries in fewer than α positions. Our main result tells when Π(κ,<α) can be embedded in Π(λ,<β). The proof involves some set-theoretic results, one about families of finite sets and one about families of ultrafilters. Partially supported by NSF grant DMS–0070723. Part of thi...