This book is a course in Stone-Priestley duality theory, with applications to logic and theoretical computer science. Our target audience are graduate students and researchers in mathematics and computer science. Our aim is to get in a fairly full palette of duality tools as directly and quickly as possible, then to illustrate and further elaborate these tools within the setting of three emblematic applications: semantics of propositional logics, domain theory in logical form, and the theory of profinite monoids for the study of regular languages and automata. This preprint version contains the first part of the book, a graduate level `crash course' in duality theory as it is practiced now, and a chapter on applications to domain theory.
翻译:这本书是一门具有逻辑和理论计算机科学应用的Ston-Priestley两极理论课程。 我们的目标受众是数学和计算机科学的研究生和研究人员。 我们的目标是尽可能直接和迅速地进入一个相当完整的双极工具宝盘,然后在三个标志性应用的设置中说明和进一步阐述这些工具:理论逻辑的语义、逻辑形式的域论,以及用于研究常规语言和自动模型的绝对单一理论。 这个预印版包含这本书的第一部分、目前实践的双重理论的研究生级“崩溃课程”和关于域论应用的一章。