Canonical extensions

Steven Givant
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Steven Givant: Mills College, Department of Mathematics

Chapter Chapter 14 in Advanced Topics in Relation Algebras, 2017, pp 1-100 from Springer

Abstract: Abstract The structural analysis of a relation algebra is simplified substantially when the algebra in question is complete and atomic. Of course, not all relation algebras are complete or atomic, but it is a happy state of affairs that every relation algebra can be extended to one that is. The purpose of this chapter is to study the most important of these extensions. The construction actually goes through in the context of arbitrary Boolean algebras with operators. For the sake of concreteness and to simplify notation, we always take the similarity type of the algebras under discussion to be the same as the similarity type of relation algebras; but it should be obvious from the presentation how to extend the development to Boolean algebras with operators of arbitrary ranks.

Date: 2017
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DOI: 10.1007/978-3-319-65945-9_1

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