A model of the generic Vopěnka principle in which the ordinals are not Mahlo

DOI10.1007/s00153-018-0632-5OpenAlexW2622696219MaRDI QIDQ1712940

Victoria Gitman, Joel David Hamkins

Publication date: 24 January 2019

Published in: Archive for Mathematical Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.00843

zbMATH Keywords

remarkable cardinalsgeneric Vopenka principlevirtual large cardinals

Mathematics Subject Classification ID

Consistency and independence results (03E35) Large cardinals (03E55)

Related Items (4)

THE CONSISTENCY STRENGTH OF THE PERFECT SET PROPERTY FOR UNIVERSALLY BAIRE SETS OF REALS ⋮ Model theoretic characterizations of large cardinals ⋮ Generic Vopěnka cardinals and models of ZF with few \(\aleph _1\)-Suslin sets ⋮ WEAKLY REMARKABLE CARDINALS, ERDŐS CARDINALS, AND THE GENERIC VOPĚNKA PRINCIPLE

Cites Work

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• \(C ^{(n)}\)-cardinals
• Generic Vopěnka's principle, remarkable cardinals, and the weak proper forcing axiom
• Virtual large cardinals
• Proper forcing and remarkable cardinals II
• Ideals and Generic Elementary Embeddings
• Strong axioms of infinity and elementary embeddings
• ON C⁽ⁿ⁾-EXTENDIBLE CARDINALS
• Kelley–Morse set theory does not prove the class Fodor principle
• On Colimits and Elementary Embeddings
• Superstrong and other large cardinals are never Laver indestructible

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