Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · math/9803167

Strongly almost disjoint sets and weakly uniform bases

Zoltán Balogh·Sheldon W. Davis·Winfried Just·Saharon Shelah·Paul J. Szeptycki
View original source ↗Read source document ↗Export metadata ↓

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 T_1-space with a weakly uniform base has a point-countable base.''

Explore related subjects

math.LOmath.GN

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Zoltán Balogh, Sheldon W. Davis, Winfried Just, Saharon Shelah, Paul J. Szeptycki. 1998-03-15. Strongly almost disjoint sets and weakly uniform bases. https://arxiv.org/abs/math/9803167

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Amenable C-sequences and ineffability in L

We give a relative consistency counterexample to the conjecture of Inamdar and Rinot that every regular uncountable cardinal carrying no amenable C-sequence is ineffable in the constructible universe L. The existence of a $Π^2_1$-indescribable cardinal is equiconsistent with the existence of a $Π^2_1$-indescribable cardinal carrying no amenable C-sequence and not ineffable in L. For every ground-model C-sequence on a weakly compact cardinal $κ$, generalized Hechler forcing adds a club D with $D\capβ\subseteq C_β$ at stationarily many inaccessible indices. We use this capture theorem in an iteration of length $κ^+$ after Johnstone's local lottery preparation.

math.LO↗
arXiv2026

Omitting Types for Infinitary Real-Valued Logic: A Topological Perspective

For countable vocabularies, we extend the omitting types theorem for countable fragments of infinitary logic to Keisler's general real-valued structures by proving that the space of Henkin types of each such fragment is Čech-complete. The structures interpret function symbols arbitrarily and predicate symbols by bounded real-valued functions, while each formula carries a bound of its own. This extends the setting of Eagle's theorem from metric structures with a prescribed master metric to general structures whose vocabulary prescribes the sorts and bounds of the symbols. Following Keisler and Miller's treatment of logic without equality, we build models from closed terms. Morley's Baire category method then gives every satisfiable theory on a countable fragment a model with countable sorts omitting any countable family of types whose closed-term instances have empty interior in the space of Henkin types satisfying the theory.

math.LO↗
arXiv2026

Friedman--Stanley cofinality without Borel completeness

Friedman and Stanley asked whether an invariant Borel class of countable structures must be Borel complete whenever every countable level of their hierarchy reduces to it. We construct a counterexample in one fixed countable language. The structural counterexample and its principal supporting results have been formalized in Lean~4 and it is available on github.

math.LO↗