Sh:720
- Kojman, M., & Shelah, S. (2001). Fallen cardinals. Ann. Pure Appl. Logic, 109(1-2), 117–129. arXiv: math/0009079 DOI: 10.1016/S0168-0072(01)00045-8 MR: 1835242
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Abstract:
We prove that for every singular cardinal \mu of cofinality \omega, the complete Boolean algebra {\rm comp}{\mathcal P}_\mu(\mu) contains as a complete subalgebra an isomorphic copy of the collapse algebra {\rm Comp}\;{\rm Col}(\omega_1,\mu^{\aleph_0}). Consequently, adding a generic filter to the quotient algebra {\mathcal P}_\mu(\mu)={\mathcal 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.
- Version 2001-06-27_11 (11p) published version (13p)
Bib entry
@article{Sh:720,
author = {Kojman, Menachem and Shelah, Saharon},
title = {{Fallen cardinals}},
journal = {Ann. Pure Appl. Logic},
fjournal = {Annals of Pure and Applied Logic},
volume = {109},
number = {1-2},
year = {2001},
pages = {117--129},
issn = {0168-0072},
mrnumber = {1835242},
mrclass = {03G05 (03E04 03E40 54D80)},
doi = {10.1016/S0168-0072(01)00045-8},
note = {\href{https://arxiv.org/abs/math/0009079}{arXiv: math/0009079}},
dedication = {Dedicated to Petr Vop\v{e}nka},
arxiv_number = {math/0009079}
}