Fallen Cardinals
| dc.creator | Kojman, Menachem | |
| dc.creator | Shelah, Saharon | |
| dc.date | 2000-09-07 | |
| dc.date.accessioned | 2026-07-07T04:37:16Z | |
| dc.date.available | 2026-07-07T04:37:16Z | |
| dc.description | We 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.identifier | https://arxiv.org/abs/math/0009079 | |
| dc.identifier | http://arxiv.org/abs/math/0009079 | |
| dc.identifier | Ann. Pure Appl. Logic 109 No. 1-2 (2001) 117--129 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59891 | |
| dc.subject | Logic | |
| dc.title | Fallen Cardinals | |
| dc.type | text |