Some consequences of reflection on the approachability ideal

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dc.creatorSharon, Assaf
dc.creatorViale, Matteo
dc.date2008-04-04
dc.date.accessioned2026-07-07T09:30:31Z
dc.date.available2026-07-07T09:30:31Z
dc.descriptionWe study the approachability ideal I[κ^+] in the context of large cardinals properties of the regular cardinals below a singular κ. As a guiding example consider the approachability ideal I[\aleph_{ω+1}] assuming that \aleph_ωis strong limit. In this case we obtain that club many points in \aleph_{ω+1} of cofinality \aleph_n for some n>1 are approachable assuming the joint reflection of countable families of stationary subsets of \aleph_n. This reflection principle holds under Martin's maximum for all n>1 and for each n>1 is equiconsistent with \aleph_n being weakly compact in L. This characterizes the structure of the approachability ideal I[\aleph_{ω+1}] in models of Martin's maximum.
dc.description11 pages, updated versions available at the author's webpage
dc.identifierhttps://arxiv.org/abs/0804.0775
dc.identifierhttp://arxiv.org/abs/0804.0775
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/158147
dc.subjectLogic
dc.subjectCommutative Algebra
dc.subject03E04, 03E55
dc.titleSome consequences of reflection on the approachability ideal
dc.typetext

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