Remarks on quotient algebras
Ryszard Frankiewicz, S{\l}awomir Szczepaniak
TL;DR
This paper investigates the structure of quotient Boolean algebras using cardinal invariants, rederives key results on atomless ideals, and simplifies existing proofs for better understanding.
Contribution
It provides new simplified proofs of known results on quotient Boolean algebras and atomless ideals, enhancing theoretical understanding.
Findings
Reproved results of Gitik and Shelah on atomless ideals
Simplified proofs of structure theorems for quotient Boolean algebras
Enhanced theoretical framework for cardinal invariants in Boolean algebras
Abstract
The structure of quotient Boolean algebras in terms of cardinal invariants is investigated. Some results of Gitik and Shelah regarding atomless ideals are reproved and proofs are significantly simplified.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Advanced Topics in Algebra · Rings, Modules, and Algebras