Hausdorff Gaps and Limits

Abstract

Part 1 Boolean algebras: formulas atoms complete algebras homomorphism and filters ultrafilters extending a homomorphism chains and antichains problems. Part 2 Gaps and limits: dominance Hausdorff gaps the Parovicenko theorem types of gaps and limits problems. Part 3 Stone spaces: the stone representation subalgebras and homomorphisms zero-sets the stone-cech compactification spaces of uniform ultrafilters strongly zero-dimensional spaces extremally disconnected spaces problems. Part 4 F-spaces: extending a function characterization of countable gaps construction of Parovicenko spaces closed sets in the space omega* on the Parovicenko theorem on P-sets in the space omega* character of points problems. Part 5 Pi-base matrix: points. Part 6 Inhomogeneity: Kunen's points a matrix of independent sets countable sets in F-spaces inhomogeneity of products of compact spaces problems. Part 7 Extending of continuous functions: weak Lindelhof property a long convergent sequence strongly discrete sets problems. Part 8 The Martin axiom: continuous images the space beta[omega1] on the Parovicenko theorem gaps homomorphisms of C(X) problems. Part 9 Partitions of antichains: partition of algebras complete algebras partition algebras under MA more on partition algebras problems. Part 10 Small P-sets in omega*: proper forcing on P-filters with the ccc problems. Part 11 Forcing: set theory and its models forcing complete embeddings cardinal numbers selected models iterated forcing the Martin axiom.