Abstract
This chapter presents the study of the interplay between recursion in higher types and transfinite recursion. The chapter introduces the theory of partial continuous functionals, based on Scott's notion of an information system. The partial continuous functionals are central for any the analysis of higher type computability, which is based on the rather natural assumption that any computation ought to be finite. The reason is simply that they form the mathematically appropriate domain of a computable functional. The chapter also presents the collapsing results and discusses the extended Grzegorczyk hierarchy. An introduction to partial continuous functional and some general material concerning computability in higher types is also presented in the chapter. The chapter discusses bounded fixed point operators and concerns elimination of detours through higher types by transfinite recursion.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Studies in Logic and the Foundations of Mathematics
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
