Fallen Cardinals

dc.creatorKojman, Menachem
dc.creatorShelah, Saharon
dc.date2000-09-07
dc.date.accessioned2026-07-07T04:37:16Z
dc.date.available2026-07-07T04:37:16Z
dc.descriptionWe prove that for every singular cardinal mu of cofinality omega, the complete Boolean algebra compP_mu(mu) contains as a complete subalgebra an isomorphic copy of the collapse algebra Comp Col(omega_1,mu^{aleph_0}). Consequently, adding a generic filter to the quotient algebra P_mu(mu)=P(mu)/[mu]^{<mu} collapses mu^{aleph_0} to aleph_1. Another corollary is that the Baire number of the space U(mu) of all uniform ultrafilters over mu is equal to omega_2. The corollaries affirm two conjectures by Balcar and Simon. The proof uses pcf theory.
dc.identifierhttps://arxiv.org/abs/math/0009079
dc.identifierhttp://arxiv.org/abs/math/0009079
dc.identifierAnn. Pure Appl. Logic 109 No. 1-2 (2001) 117--129
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59891
dc.subjectLogic
dc.titleFallen Cardinals
dc.typetext

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