Combinatorial Characterization of Supercompact Cardinals

DOI10.2307/2039718zbMath0279.02050OpenAlexW4242733374MaRDI QIDQ4404891

Menachem Magidor

Publication date: 1974

Full work available at URL: https://doi.org/10.2307/2039718

Mathematics Subject Classification ID

Large cardinals (03E55)

Related Items (31)

Partition relations for \(\kappa\)-normal ideals on \(P_{\kappa}(\lambda)\) ⋮ Small embedding characterizations for large cardinals ⋮ The structure of ineffability properties of \(P_{\kappa}\lambda\) ⋮ THE STRONG TREE PROPERTY AT SUCCESSORS OF SINGULAR CARDINALS ⋮ THE CONSISTENCY STRENGTH OF THE PERFECT SET PROPERTY FOR UNIVERSALLY BAIRE SETS OF REALS ⋮ The super tree property at the successor of a singular ⋮ SUBCOMPACT CARDINALS, TYPE OMISSION, AND LADDER SYSTEMS ⋮ Indestructibility of some compactness principles over models of \(\mathsf{PFA} \) ⋮ The strong tree property and weak square ⋮ On the universality of the nonstationary ideal ⋮ Strong tree properties, Kurepa trees, and guessing models ⋮ Rado’s Conjecture and its Baire version ⋮ Necessary and sufficient conditions for the existence of an \(n\)-subtle cardinal ⋮ On the consistency strength of the proper forcing axiom ⋮ Guessing models and generalized Laver diamond ⋮ The combinatorial essence of supercompactness ⋮ Two-cardinal versions of weak compactness: partitions of pairs ⋮ Notes on the partition property of \({\mathcal{P}_\kappa\lambda}\) ⋮ Strong tree properties for two successive cardinals ⋮ The ineffable tree property and failure of the singular cardinals hypothesis ⋮ Characterizing large cardinals through Neeman's pure side condition forcing ⋮ HIERARCHIES OF FORCING AXIOMS, THE CONTINUUM HYPOTHESIS AND SQUARE PRINCIPLES ⋮ Characterizing large cardinals in terms of layered posets ⋮ Closure Sets of Functions and a Hierarchy of Filters ⋮ A model of Cummings and Foreman revisited ⋮ Patching ideal families on \({\mathcal P}_\kappa\lambda\) ⋮ ITP, ISP, AND SCH ⋮ Maximum deconstructibility in module categories ⋮ An Extension of the Closed Unbounded Filter ⋮ The tree property at both ℵ_ω+1and ℵ_ω+2 ⋮ Two-cardinal versions of weak compactness: partitions of triples

Cites Work

• Unnamed Item
• On the role of supercompact and extendible cardinals in logic
• Strong axioms of infinity and elementary embeddings
• Some combinatorial problems concerning uncountable cardinals

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