Smoke and mirrors: combinatorial properties of small cardinals equiconsistent with huge cardinals

DOI10.1016/j.aim.2009.05.006zbMath1178.03068OpenAlexW1985784884MaRDI QIDQ838140

Matthew Foreman

Publication date: 21 August 2009

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2009.05.006

zbMATH Keywords

forcinglarge cardinalsChang's conjectureinner modelsnon-stationary ideal

Mathematics Subject Classification ID

Consistency and independence results (03E35) Inner models, including constructibility, ordinal definability, and core models (03E45) Large cardinals (03E55)

Related Items (9)

THE DIAGONAL STRONG REFLECTION PRINCIPLE AND ITS FRAGMENTS ⋮ Inner models with large cardinal features usually obtained by forcing ⋮ On the consistency strength of the proper forcing axiom ⋮ PFA and ideals on \(\omega_{2}\) whose associated forcings are proper ⋮ CHANG’S CONJECTURE, GENERIC ELEMENTARY EMBEDDINGS AND INNER MODELS FOR HUGE CARDINALS ⋮ Global Chang's conjecture and singular cardinals ⋮ The diagonal reflection principle ⋮ Huge reflection ⋮ On the consistency of local and global versions of Chang’s Conjecture

Cites Work

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• Large cardinals and definable counterexamples to the continuum hypothesis
• Calculating quotient algebras of generic embeddings
• Large Cardinals and Strong Model Theoretic Transfer Properties
• Saturated ideals
• Precipitous towers of normal filters
• THE CLUB GUESSING IDEAL: COMMENTARY ON A THEOREM OF GITIK AND SHELAH

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