Ramsey ultrafilters and the reaping number - Con(\({\mathfrak r}<{\mathfrak u}\))

DOI10.1016/0168-0072(90)90063-8zbMath0721.03032OpenAlexW2090375774MaRDI QIDQ2640594

Saharon Shelah, Martin Goldstern

Publication date: 1990

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0168-0072(90)90063-8

zbMATH Keywords

iterated forcinggeneric realsreaping numbergeneric modelsRamsey ultrafiltersbase for an ultrafilterultrafilter on \(\omega \)

Mathematics Subject Classification ID

Consistency and independence results (03E35) Other combinatorial set theory (03E05)

Related Items (14)

HIGHER INDEPENDENCE ⋮ Partition theorems from creatures and idempotent ultrafilters ⋮ Cichoń's diagram and localisation cardinals ⋮ PARTITION FORCING AND INDEPENDENT FAMILIES ⋮ Cohen preservation and independence ⋮ A more direct proof of a result of Shelah ⋮ On minimal \(\pi\)-character of points in extremally disconnected compact spaces ⋮ Rosenthal families, pavings, and generic cardinal invariants ⋮ Asymmetric tie-points and almost clopen subsets of $\mathbb {N}^*$ ⋮ Reaping number and \(\pi\)-character of Boolean algebras ⋮ CON(\(\mathfrak u>\mathfrak i\)) ⋮ Free sequences in \({\mathscr{P}}( \omega) /\mathrm{fin}\) ⋮ Parametrized $\diamondsuit $ principles ⋮ Ultrafilters on 𝜔-their ideals and their cardinal characteristics

Cites Work

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• A dual form of Ramsey's theorem
• There may be simple \(P_{\aleph _ 1}\)- and \(P_{\aleph _ 2}\)-points and the Rudin-Keisler ordering may be downward directed
• Proper forcing
• A more direct proof of a result of Shelah
• Some unifying principles in Ramsey theory
• Finite sums from sequences within cells of a partition of N
• A short proof of Hindman's theorem
• Families of sets and functions

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