A direct proof of a theorem of Jech and Shelah on PCF algebras
Abstract By using an argument based on the structure of the locally compact scattered spaces, we prove in a direct way the following result shown by Jech and Shelah: there is a family {Bα: α < ω1} of subsets of ω1 such that the following conditions are satisfied: (a) max B α - α, (b) if α ∈ B β then Bα ⊆ B β, (c) if δ ≤ α and δ is a limit ordinal then Bα ∩ δ is not in the ideal generated by the sets Bβ, β < α, and by the bounded subsets of δ, (d) there is a partition {An: n ∈ ω} of ω1 such that for every α and every n, B α ∩ A n is finite.
Saved in:
| Main Author: | |
|---|---|
| Format: | Digital revista |
| Language: | English |
| Published: |
Universidad Nacional de Colombia y Sociedad Colombiana de Matemáticas
2018
|
| Online Access: | http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0034-74262018000200131 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|