一句话:为有限布尔代数在分配格范畴中内射这一断言给出构造性意义,并将 Sikorski 扩张定理转为语法保守结果。
本文为“每个有限布尔代数都是分配格范畴中的内射对象”这一断言赋予构造性意义。作者采用 Scott 的蕴含关系(entailment relation)框架,描述有限布尔代数的 Sikorski 扩张定理,并将其转化为一个语法保守性结果。作为副产品,该结果有助于证明若干相关的经典原则。贡献在于在构造性语境中澄清 Sikorski 扩张定理,并揭示其与保守性之间的语法联系。
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 several related classical principles.