This article re-examines Lawvere's abstract, category-theoretic proof of the fixed-point theorem whose contrapositive is a `universal' diagonal argument. The main result is that the necessary axioms for both the fixed-point theorem and the diagonal argument can be stripped back further, to a semantic analogue of a weak substructural logic lacking weakening or exchange.
翻译:本条重新审查了Lawvere关于固定点理论的抽象、分类理论证据,该理论的相对性是`普遍'对角论,其主要结果是,固定点理论和对角论的必要正义可以进一步被剥去,以至一种缺乏削弱或交换的薄弱次级结构逻辑的语义相似性。