Constructive meaning is given to the assertion that every finite Boolean algebra is an injective object in the category of distributive lattices. To this end, we employ Scott's notion of entailment relation, in which context we describe Sikorski's extension theorem for finite Boolean algebras and turn it into a syntactical conservation result. As a by-product, we can facilitate proofs of related classical principles.

EXTENSION BY CONSERVATION. SIKORSKI'S THEOREM

Rinaldi, D;Wessel, D
2018-01-01

Abstract

Constructive meaning is given to the assertion that every finite Boolean algebra is an injective object in the category of distributive lattices. To this end, we employ Scott's notion of entailment relation, in which context we describe Sikorski's extension theorem for finite Boolean algebras and turn it into a syntactical conservation result. As a by-product, we can facilitate proofs of related classical principles.
2018
entailment relations; distributive lattices; constructive mathematics
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/990380
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