# Sh:476

- Jech, T. J., & Shelah, S. (1996).
*Possible PCF algebras*. J. Symbolic Logic,**61**(1), 313–317. arXiv: math/9412208 DOI: 10.2307/2275613 MR: 1380692 -
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. - 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}, doi = {10.2307/2275613}, mrclass = {03E10 (03E40)}, mrnumber = {1380692}, mrreviewer = {James Baumgartner}, doi = {10.2307/2275613}, note = {\href{https://arxiv.org/abs/math/9412208}{arXiv: math/9412208}}, arxiv_number = {math/9412208} }