# Sh:476

• Jech, T. J., & Shelah, S. (1996). Possible PCF algebras. J. Symbolic Logic, 61(1), 313–317.
• Abstract:
There exists a family \{B_{\alpha}\}_{\alpha<\omega_1} of sets of countable ordinals such that 1) \max B_{\alpha}=\alpha, 2) if \alpha\in B_{\beta} then B_{\alpha}\subseteq B_{\beta}, 3) if \lambda\leq \alpha and \lambda is a limit ordinal then B_{\alpha}\cap\lambda is not in the ideal generated by the B_{\beta}, 4) \beta< \alpha, and by the bounded subsets of \lambda, 5) there is a partition \{A_n\}_{n=0}^{\infty} of \omega_1 such that for every \alpha and every n, B_{\alpha}\cap A_n is finite.
• Version 1995-03-23_10 (7p) published version (6p)
Bib entry
@article{Sh:476,
author = {Jech, Thomas J. and Shelah, Saharon},
title = {{Possible PCF algebras}},
journal = {J. Symbolic Logic},
fjournal = {The Journal of Symbolic Logic},
volume = {61},
number = {1},
year = {1996},
pages = {313--317},
issn = {0022-4812},
mrnumber = {1380692},
mrclass = {03E10 (03E40)},
doi = {10.2307/2275613},
note = {\href{https://arxiv.org/abs/math/9412208}{arXiv: math/9412208}},
arxiv_number = {math/9412208}
}