Adam Kwela

A note on a new ideal

Abstract In this paper we study a new ideal WR . The main result is the following: an ideal is not weakly Ramsey if and only if it is above WR in the Katětov order. Weak Ramseyness was introduced by Laflamme in order to characterize winning strategies in a certain game. We apply result of Natkaniec and Szuca to conclude that WR is critical for ideal convergence of sequences of quasi-continuous functions. We study further combinatorial properties of WR and weak Ramseyness. Answering a question of Filipow et al. we show that WR is not 2-Ramsey, but every ideal on ω isomorphic to WR is Mon (every sequence of reals contains a monotone subsequence indexed by an I -positive set).

Ideal equal Baire classes

Abstract For any Borel ideal we characterize ideal equal Baire system generated by the families of continuous and quasi-continuous functions, i.e., the families of ideal equal limits of sequences of continuous and quasi-continuous functions.

Homogeneous ideals on countable sets

We say that an ideal

Ideal-like properties of generalized microscopic sets

{\mathcal{I}}

Combinatorics of ideals --- selectivity versus density

I on

Haar-smallest sets.

{\omega}