Depth of Boolean algebras
Saharon Shelah, Shimon Garti
TL;DR
This paper establishes a theorem relating the depth of ultraproducts of Boolean algebras to the depths of individual algebras, addressing an open problem posed by Monk.
Contribution
It provides a partial solution to an open problem about the relationship between ultraproducts and component Boolean algebra depths.
Findings
The depth of ultraproducts can be characterized in terms of component depths.
The theorem partially answers Monk's open problem.
New insights into the structure of Boolean algebra ultraproducts.
Abstract
We prove a Theorem about the relationship between the Depth of the ultraproduct of Boolean algebras, divided by an ultrafilter, and the products of the depths of each component. This answers (partly) an open problem of Monk.
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