Computability Computable Functions Logic and the Foundations of Math

This book should be of interest to intermediate mathematics undergraduates; postgraduates in theoretical computer science/philosophy of mathematics.

Philosophy and mathematics. Some paradoxes. Whole numbers. Functions. An introduction to the nature of a proof. Infinite collections? Hilbert: on the infinite. Computability. Turing machines. The most amazing fact and Church's thesis. Primitive recursive functions. The Grzegorczyk hierarchy. Multiple recursion and recursion on order types. The least search operator. Partial recursion functions. Numbering the partial recursive functions. Listability. Turing machine computable = partial recursive. Logic and arithmetic, part 1: propositional logic. Logic and arithmetic, part 2: a review. Logic and arithmetic, part 3: first-order arithmetic. Functions representable in formal arithmetic. The undecidability of arithmetic. The unprovability of consistency. Church's thesis. Constructivist view of mathematics. Bibliography. Index of notation. Index.

Richard .L. Epstein (University of Campinas, Berkeley, CA, USA) (Author) , Walter Alexandr Carnielli (State University of Campinas, Brazil) (Author)