The ultrafilter number for singular cardinals

DOI10.1007/s10474-012-0245-0zbMath1289.03030arXiv1201.1713OpenAlexW3098027846MaRDI QIDQ2434151

Saharon Shelah, Shimon Garti

Publication date: 17 February 2014

Published in: Acta Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.1713

zbMATH Keywords

ultrafilter numbercardinal invariantspcf theorysingular cardinalslarge cardinalrelative consistency

Mathematics Subject Classification ID

Consistency and independence results (03E35) Large cardinals (03E55) Other combinatorial set theory (03E05) Cardinal characteristics of the continuum (03E17) Ordered sets and their cofinalities; pcf theory (03E04)

Related Items (11)

Cardinal characteristics at \(\aleph_\omega\) ⋮ INDESTRUCTIBILITY OF THE TREE PROPERTY ⋮ A Galvin-Hajnal theorem for generalized cardinal characteristics ⋮ A uniform ultrafilter over a singular cardinal with a singular character ⋮ Remarks on generalized ultrafilter, dominating and reaping numbers ⋮ More on uniform ultrafilters over a singular cardinal ⋮ Partition calculus and cardinal invariants ⋮ On the spectrum of characters of ultrafilters ⋮ A small ultrafilter number at smaller cardinals ⋮ Questions on generalised Baire spaces ⋮ Small \(\mathfrak{u}(\kappa )\) at singular \(\kappa\) with compactness at \(\kappa^{++}\)

Cites Work

• The character spectrum of \(\beta \mathbb N\)
• Shelah's pcf theory and its applications
• A strong polarized relation
• Combinatorial Cardinal Characteristics of the Continuum
• Cardinal Arithmetic
• Prikry-Type Forcings

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