Functional reducts of Boolean algebras
Bertalan Bodor, Kende Kalina, Csaba Szab\'o
TL;DR
This paper classifies specific reducts of the countable atomless Boolean algebra, called functional reducts, establishing that there are exactly 13 such structures up to first-order interdefinability.
Contribution
It provides a complete classification of functional reducts of the countable atomless Boolean algebra, identifying exactly 13 distinct structures.
Findings
Exactly 13 functional reducts up to first-order interdefinability
Complete classification of these reducts
Advances understanding of Boolean algebra structures
Abstract
In this paper we classify some special reducts of the countable atomless Boolean algebra which we call functional reducts. We prove that there are exactly such structures up to first order interdefinability.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Rings, Modules, and Algebras · Advanced Algebra and Logic