Combinatorics of filters and ideals Page 42 Contemporary Mathematics Contemporary
Mathematics Volume 533 , 2010 Contemporary Mathematics Volume 533 , 2011 Combinatorics …

We study the Katětov order on Borel ideals. We prove two structural theorems (dichotomies),
one for Borel ideals, the other for analytic P-ideals. We isolate nine important Borel ideals …

MATHIAS FORCING AND COMBINATORIAL COVERING PROPERTIES OF FILTERS §1.
Introduction. A subset F of [ ] is called a filter if F c Page 1 The Journal of Symbolic Logic Volume …

We construct a model in which there exists a refining matrix of regular height λ larger than h \documentclass[12pt]{minimal}
\usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} …

If F is a filter on ω, we say that F is Canjar if the corresponding Mathias forcing does not add
a dominating real. We prove that any Borel Canjar filter is F σ, solving a problem of Hrušák …

We prove that every MAD family can be destroyed by a proper forcing that preserves P-
points. With this result, we prove that it is consistent that ω 1= u< a, solving a nearly 20 year …

CANJAR FILTERS Ⅱ : PROOFS OF b<s AND b<a REVISITED Page 1 CANJAR FILTERS :
PROOFS OF $\mathfrak{b}<\epsilon$ AND $\mathfrak{b}<\mathfrak{a}$ REVISITED OSVALDO …

This paper investigates the combinatorial property of ultrafilters where the Mathias forcing
relativized to them does not add dominating reals. We prove that the characterization due to …

TOWERS IN FILTERS, CARDINAL INVARIANTS, AND LUZIN TYPE FAMILIES §1. Introduction.
Let us denote Fin the Fréchet ideal on , ie Page 1 The Journal of Symbolic Logic Volume 83 …

We study some strong combinatorial properties of $\textsf {MAD} $ families. An ideal
$\mathcal {I} $ is Shelah-Stepr\={a} ns if for every set $ X\subseteq {\left [\omega\right]}^{< …