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Notes on countably generated complete Boolean algebras

2016/11/08 by Mohammad Golshani, Golshani, Mohammad
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.1611.02694

openalex publication_date 2016/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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