Notes on countably generated complete Boolean algebras
Logic
2016-11-10 v1
Abstract
We give a necessary and sufficient condition for an atomless Boolean algebra to be countably generated, and use it to give new proofs of some some know facts due to Gaifman-Hales and Solovay and also due to Jech, Kunen and Magidor. We also show that Jensen's coding theorem can be used to provide cardinal preserving countably generated complete Boolean algebras of arbitrary large cardinality. This answers a question of Jech [5] from 1976.
Cite
@article{arxiv.1611.02694,
title = {Notes on countably generated complete Boolean algebras},
author = {Mohammad Golshani},
journal= {arXiv preprint arXiv:1611.02694},
year = {2016}
}
Comments
Preliminary version