TL;DR
This paper explores the concept of multiple gaps, which are sets of ideals in Boolean algebra that cannot be separated, focusing on their properties within the algebra of natural numbers modulo finite sets.
Contribution
It introduces and analyzes various types of multiple gaps in the Boolean algebra of subsets of natural numbers modulo finite sets, expanding understanding of their structure.
Findings
Characterization of different types of multiple gaps
Identification of properties preventing separation of ideals
Insights into the structure of Boolean algebra in this context
Abstract
We consider the notion of multiple gap as a finite set of ideals that cannot be separated. We study the different types of such objects that can be found in the Boolean algebra of subsets of the natural numbers modulo finite sets.
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Taxonomy
TopicsAdvanced Algebra and Logic · Advanced Topology and Set Theory · Rings, Modules, and Algebras