Techniques for approaching the dual Ramsey property in the projective hierarchy

We define the dualizations of objects and concepts which are essential for investigating the Ramsey property in the first levels of the projective hierarchy, prove a forcing equivalence theorem for dual Mathias forcing and dual Laver forcing, and show that the Harrington-Kechris techniques for proving the Ramsey property from determinacy work in the dualized case as well

Some new directions in infinite-combinatorial topology

We give a light introduction to selection principles in topology, a young subfield of infinite-combinatorial topology. Emphasis is put on the modern approach to the problems it deals with. Recent results are described, and open problems are stated. Some results which do not appear elsewhere are also included, with proofs.Comment: Small update

Norms on possibilities I: forcing with trees and creatures

We present a systematic study of the method of "norms on possibilities" of building forcing notions with keeping their properties under full control. This technique allows us to answer several open problems, but on our way to get the solutions we develop various ideas interesting per se.These include a new iterable condition for ``not adding Cohen reals'' (which has a flavour of preserving special properties of p-points), new intriguing properties of ultrafilters (weaker than being Ramsey but stronger than p-point) and some new applications of variants of the PP--property.Comment: accepted for Memoirs of the Amer. Math. So

Selection principles in mathematics: A milestone of open problems

We survey some of the major open problems involving selection principles, diagonalizations, and covering properties in topology and infinite combinatorics. Background details, definitions and motivations are also provided.Comment: Small update