Strongly almost disjoint sets and weakly uniform bases

1998/03/15 by Zoltán M. Balogh, Zoltán Balogh, Sheldon W. Davis +8
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO) #math.GN #math.LO

paper · pdf · doi:10.48550/arxiv.math/9803167

published as Trans. Amer. Math. Soc. 352 No. 11 (2000) 4971--4987

arxiv created 1998/03/15 · openalex publication_date 1998/03/15 · arxiv updated 2016/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A combinatorial principle CECA is formulated and its equivalence with GCH+ certain weakenings of Box_lambda for singular lambda is proved. CECA is used to show that certain ``almost point- < tau'' families can be refined to point- < tau families by removing a small set from each member of the family. This theorem in turn is used to show the consistency of ``every first countable T₁-space with a weakly uniform base has a point-countable base.''

Related

• A weak set theory that proves its own consistency
• The ultrafilter and almost disjointness numbers
• More Set-theory around the weak Freese-Nation property
• Strongly almost disjoint families, II
• Resolvability vs. almost resolvability