Depth^+ and Length^+ of Boolean algebras
Shimon Garti, Saharon Shelah
TL;DR
This paper investigates the cardinal invariants Depth^+ and Length^+ on Boolean algebras, establishing new inequalities between their product and the invariants of product algebras within ZFC.
Contribution
It introduces a strict inequality between the product of invariants and the invariant of the product algebra for many singular cardinals, proven in ZFC.
Findings
Established strict inequalities for singular cardinals
Proved results within ZFC framework
Enhanced understanding of invariants in Boolean algebras
Abstract
Let inv denote the cardinal invariants Depth^+ and Length^+ on Boolean algebras. For many singular cardinals we create a strict inequality between the product of the inv values and the inv of the product algebra. The proof holds in ZFC.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Mathematical and Theoretical Analysis