Selective ultrafilters and homogeneity

Selective Ultrafilters on FIN

We consider selective ultrafilters on the collection FIN of all finite nonempty subsets of N. If countablesupport side-by-side Sacks forcing is applied, then every selective ultrafilter in the ground model generates a selective ultrafilter in the extension. We also show that selective ultrafilters localizes the Parametrized Milliken Theorem, and that selective ultrafilters are Ramsey.

Walks on Countable Ordinals and Selective Ultrafilters

In our previous work we have introduced filters on the set of countable ordinals as invariants to standard characteristics of walks in this domain. In this note we examine their projections to the set of natural numbers.

Crowded and Selective Ultrafilters under the Covering Property Axiom

In the paper we formulate an axiom CPA prism, which is the most prominent version of the Covering Property Axiom CPA, and discuss several of its implications. In particular, we show that it implies that the following cardinal characteristics of continuum are equal to ω1, while c = ω2: the independence number i, the reaping number r, the almost disjoint number a, and the ultrafilter base number ...

Neighborhoods, Ultrafilters, and Canonicity

This paper will remind the reader of neighborhood semantics for modal logics, compare them with relational semantics, and then look at some questions about neighborhood semantics that have been answered, and some which are still open. We will then introduce “ultrafilter semantics,” a way of expressing all sets over a canonical frame in an ‘effable’ way. This provides us with a conceptually easy...

Ultrafilters and Abelian Groups