| Popis: |
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. |
