TL;DR
This paper constructs specific Boolean algebras demonstrating that the Length of a product can exceed the product of individual Lengths within ZFC set theory.
Contribution
It provides a ZFC-based construction showing the Length of a product algebra can be strictly larger than the product of individual Lengths, highlighting a new property in Boolean algebra theory.
Findings
Constructed Boolean algebras with Length properties
Demonstrated strict inequality between product Length and Length of product
Established results within ZFC without additional axioms
Abstract
We construct, in ZFC, a sequence of Boolean algebras for which the product of Lengths is strictly smaller than the Length of the product algebra.
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