## Journal of Symbolic Logic

### Possible PCF Algebras

#### 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 $B_\beta, \beta < \alpha$, and by the bounded subsets of $\lambda$, (4) there is a partition $\{A_n\}^\infty_{n = 0}$ of $\omega_1$ such that for every $\alpha$ and every $n, B_\alpha \cap A_n$ is finite.

#### Article information

Source
J. Symbolic Logic, Volume 61, Issue 1 (1996), 313-317.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183744942

Mathematical Reviews number (MathSciNet)
MR1380692

Zentralblatt MATH identifier
0878.03036

JSTOR