Abstract
Map theory is a foundation of mathematics based on λ-calculus instead of logic and sets, and thereby fulfills Church's original aim of introducing λ-calculus. Map theory can do anything set theory can do. In particular, all of classical mathematics is contained in may theory. In addition, and contrary to set theory, map theory has unlimited abstraction and contains a computer programming language as a natural subset. This makes map theory more suited to deal with mechanical procedures than set theory. In addition, the unlimited abstraction allows definition, e.g., of the notion of truth and the category of all categories. This paper introduces map theory, gives a number of applications and gives a relative consistency proof. To demonstrate the expressive power of map theory, the paper develops ZFC set theory within map theory.
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 callDisclaimer: 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.
