Forcing Axioms, Supercompact Cardinals, Singular Cardinal Combinatorics

DOI10.2178/bsl/1208358846zbMath1150.03015OpenAlexW1989130402MaRDI QIDQ5387298

Matteo Viale

Publication date: 8 May 2008

Published in: Bulletin of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/9f9c75489d33b13a7906d1ca79a63f5de4c5cbbb

zbMATH Keywords

strongly compact cardinalproper forcing axiomsingular cardinal hypothesisMartin's maximum axiom

Mathematics Subject Classification ID

Consistency and independence results (03E35) Large cardinals (03E55) Other combinatorial set theory (03E05) Ordered sets and their cofinalities; pcf theory (03E04)

Cites Work

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• Chang's conjecture for \(\aleph_\omega\)
• A five element basis for the uncountable linear orders
• Martin's maximum, saturated ideals, and nonregular ultrafilters. I
• Proper forcing
• Forcing axioms and stationary sets
• On the singular cardinals problem. I
• Indexed squares
• The strength of the failure of the singular cardinal hypothesis
• ccc forcing and splitting reals
• The proper forcing axiom, Prikry forcing, and the singular cardinals hypothesis
• Iterated Cohen extensions and Souslin's problem
• COMPLETE CCC BOOLEAN ALGEBRAS, THE ORDER SEQUENTIAL TOPOLOGY, AND A PROBLEM OF VON NEUMANN
• Forcing indestructibility of set-theoretic axioms
• Collapsing successors of singulars
• Fragments of Martin's Maximum in generic extensions
• The proper forcing axiom and the singular cardinal hypothesis
• Powers of regular cardinals

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