Approachability at the second successor of a singular cardinal

DOI10.2178/JSL/1254748688zbMath1184.03046OpenAlexW1996134866MaRDI QIDQ3655253

John Krueger, M. B. Gitik

Publication date: 7 January 2010

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

Full work available at URL: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.510.4758

zbMATH Keywords

approachability idealinternally approachable

Mathematics Subject Classification ID

Consistency and independence results (03E35) Other combinatorial set theory (03E05)

Related Items (7)

Indestructibility of some compactness principles over models of \(\mathsf{PFA} \) ⋮ TREES AND STATIONARY REFLECTION AT DOUBLE SUCCESSORS OF REGULAR CARDINALS ⋮ A general Mitchell style iteration ⋮ THE EIGHTFOLD WAY ⋮ Successive failures of approachability ⋮ Some applications of mixed support iterations ⋮ Small \(\mathfrak{u}(\kappa )\) at singular \(\kappa\) with compactness at \(\kappa^{++}\)

Cites Work

• Notes on singular cardinal combinatorics
• Reflecting stationary sets and successors of singular cardinals
• On the singular cardinals problem. I
• Making the supercompactness of \(\nu\) indestructible under \(\nu\)-directed closed forcing
• Internally club and approachable
• The generalized continuum hypothesis can fail everywhere
• Internally club and approachable for larger structures
• A general Mitchell style iteration
• Adding closed cofinal sequences to large cardinals
• A new Löwenheim-Skolem theorem
• Aronszajn trees and the independence of the transfer property

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