\(C ^{(n)}\)-cardinals

DOI10.1007/s00153-011-0261-8zbMath1250.03108arXiv1908.09664OpenAlexW2019751722WikidataQ29035933 ScholiaQ29035933MaRDI QIDQ412056

Joan Bagaria

Publication date: 3 May 2012

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

Full work available at URL: https://arxiv.org/abs/1908.09664

zbMATH Keywords

reflectionsupercompact cardinalsextendible cardinals\(C ^{(n)}\)-cardinalsVopenka's principle

Mathematics Subject Classification ID

Large cardinals (03E55) Set-theoretic model theory (03C55)

Related Items (26)

LARGE CARDINALS AS PRINCIPLES OF STRUCTURAL REFLECTION ⋮ On Colimits and Elementary Embeddings ⋮ ON THE SYMBIOSIS BETWEEN MODEL-THEORETIC AND SET-THEORETIC PROPERTIES OF LARGE CARDINALS ⋮ IDENTITY CRISIS BETWEEN SUPERCOMPACTNESS AND VǑPENKA’S PRINCIPLE ⋮ Structural reflection, shrewd cardinals and the size of the continuum ⋮ Model theoretic characterizations of large cardinals ⋮ Obtaining Woodin’s cardinals ⋮ Vopěnka's principle in \(\infty\)-categories ⋮ Reflecting measures ⋮ Subcomplete forcing principles and definable well‐orders ⋮ Indestructibility of Vopěnka's principle ⋮ Elementary chains and \(C ^{(n)}\)-cardinals ⋮ A model of the generic Vopěnka principle in which the ordinals are not Mahlo ⋮ Generic Vopěnka's principle, remarkable cardinals, and the weak proper forcing axiom ⋮ Definable orthogonality classes in accessible categories are small ⋮ Ultrahuge cardinals ⋮ ON C⁽ⁿ⁾-EXTENDIBLE CARDINALS ⋮ WEAKLY REMARKABLE CARDINALS, ERDŐS CARDINALS, AND THE GENERIC VOPĚNKA PRINCIPLE ⋮ Virtual large cardinals ⋮ Weak Vopěnka's principle does not imply Vopěnka's principle ⋮ ON RESURRECTION AXIOMS ⋮ Huge reflection ⋮ The large cardinals between supercompact and almost-huge ⋮ On extensions of supercompactness ⋮ THE WEAK VOPĚNKA PRINCIPLE FOR DEFINABLE CLASSES OF STRUCTURES ⋮ MORE ON THE PRESERVATION OF LARGE CARDINALS UNDER CLASS FORCING

Cites Work

• Unnamed Item
• Implications between strong large cardinal axioms
• Definable orthogonality classes in accessible categories are small
• On the role of supercompact and extendible cardinals in logic
• Elementary embeddings and infinitary combinatorics
• Many-times huge and superhuge cardinals
• A Proof of Projective Determinacy

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