Indescribable cardinals and elementary embeddings

DOI10.2307/2274692zbMath0745.03041OpenAlexW2083775182WikidataQ56211143 ScholiaQ56211143MaRDI QIDQ3984421

Kai Hauser

Publication date: 27 June 1992

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

Full work available at URL: https://doi.org/10.2307/2274692

zbMATH Keywords

consistencyiterated forcingelementary embeddingsmaster conditiontransitive setsfailure of GCHindescribable cardinal

Mathematics Subject Classification ID

Consistency and independence results (03E35) Large cardinals (03E55) Continuum hypothesis and Martin's axiom (03E50)

Related Items (19)

Small embedding characterizations for large cardinals ⋮ The consistency strength of projective absoluteness ⋮ Diamond (on the regulars) can fail at any strongly unfoldable cardinal ⋮ Strong unfoldability, shrewdness and combinatorial consequences ⋮ Partition properties for simply definable colourings ⋮ SUBCOMPACT CARDINALS, TYPE OMISSION, AND LADDER SYSTEMS ⋮ Club stationary reflection and the special Aronszajn tree property ⋮ -definability at higher cardinals: Thin sets, almost disjoint families and long well-orders ⋮ The special Aronszajn tree property ⋮ Small models, large cardinals, and induced ideals ⋮ Characterizing large cardinals through Neeman's pure side condition forcing ⋮ The indescribability of the order of the indescribable cardinals ⋮ CLOSURE PROPERTIES OF MEASURABLE ULTRAPOWERS ⋮ Gödel's Program Revisited Part I: The Turn to Phenomenology ⋮ Forcing a \(\square(\kappa)\)-like principle to hold at a weakly compact cardinal ⋮ The proper and semi-proper forcing axioms for forcing notions that preserve ℵ₂ or ℵ₃ ⋮ Indescribable cardinals without diamonds ⋮ Partial strong compactness and squares ⋮ Adding a nonreflecting weakly compact set

Cites Work

• Iterated Cohen extensions and Souslin's problem
• Supercompact cardinals, sets of reals, and weakly homogeneous trees

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