可实现性类别
Realizability Categories
摘要：
这是作者的博士学位。论文它包含了四年来对可实现性和范畴逻辑的研究结果。主要的主题是可实现命题的公理化，以及作为伪初始对象的可实现性范畴的表征。可实现性是构造性逻辑研究中的一系列技术。某些形式的可实现性归纳出可实现性范畴，这些范畴是海廷范畴，因此具有一阶直觉主义逻辑作为内部语言。论文的公理化章节解释了如何以及在何种程度上我们可以公理化这一内部语言中的有效命题集。可实现性范畴章节解释了如何从可实现性范畴到其他范畴中找到正则函子。
英文摘要：
This is the author's Ph.D. Thesis. It contains results from four years of research into realizability and categorical logic. The main subjects are the axiomatisation of realizable propositions, and a characterization of realizability categories as pseudoinitial objects. Realizability is a collection of techniques in the study of constructive logic. Some forms of realizability induce realizability categories, which are Heyting categories and therefore have a first order intuitionistic logic as internal language. The axiomatisation chapter of the thesis explains how and to what extend we can axiomatise the set of valid propositions in this internal language. The realizability categories chapter explains how to find regular functors from realizability categories into other categories.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
