Tree \(\pi\)-bases for \(\beta N-N\) in various models

DOI10.1016/0166-8641(89)90085-0zbMath0697.54003OpenAlexW2021167136MaRDI QIDQ911086

Alan Dow

Publication date: 1989

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0166-8641(89)90085-0

zbMATH Keywords

Laver forcingParovičenko space(weak) Novák numberČech-Stone remainder of the discrete spaceforcing extensionsnon-coabsolute Parovičenko spacestree \(\pi\)-base

Mathematics Subject Classification ID

Consistency and independence results (03E35) Cardinality properties (cardinal functions and inequalities, discrete subsets) (54A25) Stone spaces (Boolean spaces) and related structures (06E15) Remainders in general topology (54D40) Consistency and independence results in general topology (54A35) Chain conditions, complete algebras (06E10) Extremally disconnected spaces, (F)-spaces, etc. (54G05)

Related Items (9)

Intersection numbers of families of ideals ⋮ Alan Dow ⋮ Games on base matrices ⋮ Continuum cardinals generalized to Boolean algebras ⋮ P-filters and Cohen, random, and Laver forcing ⋮ Adding ultrafilters by definable quotients ⋮ Base tree property ⋮ Distributivity of the algebra of regular open subsets of \(\beta\mathbb R\setminus \mathbb R\) ⋮ Property \({(\hbar)}\) and cellularity of complete Boolean algebras

Cites Work

• Co-absolutes of \(\beta N\setminus N\)
• Set theory. An introduction to independence proofs
• Spaces co-absolute with \(\beta N-N\)
• A compact F-space not co-absolute with betaN-N
• On the consistency of Borel's conjecture
• Barely Baire spaces
• The space of ultrafilters on N covered by nowhere dense sets
• Iterated perfect-set forcing
• There are no Q-Points in Laver's Model for the Borel Conjecture
• Trees, Gleason Spaces, and Coabsolutes of βN ∼N
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