The number of independent elements in the product of interval Boolean algebras

TL;DR

This paper establishes a new upper bound on the size of independent sets in the product of Boolean algebras, showing that such sets cannot exceed 2^kappa elements, refining previous bounds.

Contribution

It proves that in the product of kappa Boolean algebras, the maximum size of an independent set is 2^kappa, improving earlier known bounds.

Findings

Maximum independent set size in product of Boolean algebras is 2^kappa.

Previous bounds were 2^{2^kappa}, now improved.

Provides a solution to a problem posed by Monk.

Abstract

We prove that in the product of kappa many Boolean algebras we cannot find an independent set of more than 2^kappa elements solving a problem of Monk (earlier it was known that we cannot find more than 2^{2^kappa} but can find 2^kappa).