What makes a Stone topological algebra profinite
Jorge Almeida, Herman Goulet-Ouellet, Ond\v{r}ej Kl\'ima
TL;DR
This paper investigates the conditions under which a topological algebra on a Stone space is profinite, simplifying existing proofs and clarifying the role of syntactic congruences through various descriptions.
Contribution
It reformulates and simplifies proofs of known properties for topological algebras on Stone spaces, emphasizing syntactic congruences and their descriptions.
Findings
Identifies key properties for profiniteness of topological algebras on Stone spaces
Simplifies proofs using syntactic congruences
Clarifies the role of different descriptions of syntactic congruences
Abstract
This paper is a contribution to understanding what properties should a topological algebra on a Stone space satisfy to be profinite. We reformulate and simplify proofs for some known properties using syntactic congruences. We also clarify the role of various alternative ways of describing syntactic congruences, namely by finite sets of terms and by compact sets of continuous self mappings of the algebra.
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Taxonomy
TopicsAdvanced Algebra and Logic · Constraint Satisfaction and Optimization · Logic, Reasoning, and Knowledge