Small forcing makes any cardinal superdestructible

DOI10.2307/2586586zbMath0906.03051arXiv1607.00684OpenAlexW3104040049WikidataQ56813201 ScholiaQ56813201MaRDI QIDQ4391421

Joel David Hamkins

Publication date: 29 July 1998

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

Full work available at URL: https://arxiv.org/abs/1607.00684

zbMATH Keywords

measurabilitysupercompact cardinalsmall forcingsuperdestructible

Mathematics Subject Classification ID

Large cardinals (03E55) Other aspects of forcing and Boolean-valued models (03E40)

Related Items (16)

A hierarchy of Ramsey-like cardinals ⋮ Unnamed Item ⋮ FORCING AND THE HALPERN–LÄUCHLI THEOREM ⋮ Generic embeddings associated to an indestructibly weakly compact cardinal ⋮ Fragility and indestructibility. II ⋮ Fresh subsets of ultrapowers ⋮ CLOSURE PROPERTIES OF MEASURABLE ULTRAPOWERS ⋮ Gap forcing ⋮ Forcing a \(\square(\kappa)\)-like principle to hold at a weakly compact cardinal ⋮ Indestructibility and destructible measurable cardinals ⋮ Superstrong and other large cardinals are never Laver indestructible ⋮ Destruction or preservation as you like it ⋮ DEPENDENT CHOICE, PROPERNESS, AND GENERIC ABSOLUTENESS ⋮ Tall cardinals ⋮ A universal indestructibility theorem compatible with level by level equivalence ⋮ Large cardinals with few measures

Cites Work

• Making the supercompactness of \(\nu\) indestructible under \(\nu\)-directed closed forcing

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