The saturation of club guessing ideals

DOI10.1016/j.apal.2006.04.002zbMath1099.03040OpenAlexW2092767182MaRDI QIDQ2503411

Tetsuya Ishiu

Publication date: 14 September 2006

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

Full work available at URL: https://doi.org/10.1016/j.apal.2006.04.002

zbMATH Keywords

club guessingsaturated idealsupercompact cardinalforcing axiomWoodin cardinalrevised countable support iteration

Mathematics Subject Classification ID

Consistency and independence results (03E35) Large cardinals (03E55) Continuum hypothesis and Martin's axiom (03E50) Other combinatorial set theory (03E05)

Cites Work

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• Club guessing and the universal models
• Martin's maximum, saturated ideals, and nonregular ultrafilters. I
• Making the supercompactness of \(\nu\) indestructible under \(\nu\)-directed closed forcing
• The axiom of determinacy, forcing axioms, and the nonstationary ideal
• A perfectly normal nonrealcompact space consistent with MA\(_{\aleph_1}\)
• Nonexistence of universal orders in many cardinals
• On ideals of sets and the power set operation
• On splitting stationary subsets of large cardinals
• Ideals over uncountable sets: application of almost disjoint functions and generic ultrapowers
• On squares, outside guessing of clubs and I
• A topological test space for many set-theoretical axioms
• Proper and Improper Forcing
• Club guessing sequences and filters
• THE CLUB GUESSING IDEAL: COMMENTARY ON A THEOREM OF GITIK AND SHELAH

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