PFA and ideals on \(\omega_{2}\) whose associated forcings are proper

DOI10.1215/00294527-1716793zbMath1253.03078OpenAlexW2093527621MaRDI QIDQ1762362

Sean D. Cox

Publication date: 23 November 2012

Published in: Notre Dame Journal of Formal Logic (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.ndjfl/1348524118

zbMATH Keywords

large cardinalsidealsduality theoremPFAforcing axiomsproper forcing

Mathematics Subject Classification ID

Consistency and independence results (03E35) Large cardinals (03E55) Continuum hypothesis and Martin's axiom (03E50) Other combinatorial set theory (03E05) Generic absoluteness and forcing axioms (03E57)

Related Items (5)

FORCING AXIOMS, APPROACHABILITY, AND STATIONARY SET REFLECTION ⋮ IDEAL PROJECTIONS AND FORCING PROJECTIONS ⋮ Ultrahuge cardinals ⋮ Category forcings, 𝑀𝑀⁺⁺⁺, and generic absoluteness for the theory of strong forcing axioms ⋮ ON RESURRECTION AXIOMS

Cites Work

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• Guessing models and generalized Laver diamond
• Smoke and mirrors: combinatorial properties of small cardinals equiconsistent with huge cardinals
• Martin's maximum, saturated ideals, and nonregular ultrafilters. I
• The proper forcing axiom and stationary set reflection
• The axiom of determinacy, forcing axioms, and the nonstationary ideal
• Large cardinals and definable counterexamples to the continuum hypothesis
• Calculating quotient algebras of generic embeddings
• The diagonal reflection principle
• Iterated Forcing and Elementary Embeddings
• Ideals and Generic Elementary Embeddings
• Laver sequences for extendible and super-almost-huge cardinals
• IDEAL PROJECTIONS AND FORCING PROJECTIONS

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