Reasoning in Simple Type Theory is a collection of papers that includes reprints of eight seminal papers in this area as well as thirteen new contributed articles. For the reprints we have chosen a paper by Alonzo Church (introducing his simple theory of types), a paper by Leon Henkin (proving completeness of Church's type theory relative to Henkin's semantics) and some of the most important papers by Peter Andrews. The new articles were contributed by Peter Andrews and his students and collaborators as well as a number of researchers his work has influenced. The volume intends to show the...

Hilbert and Bernays' 'Grundlagen der Mathematik' appeared in two volumes in 1934 and 1939, a second edition in 1968 and 1970. It offers a foundation for proof theory and is a major source on David Hilbert's formalist programme, Paul Bernays' philosophy, the epsilon operator, and much more. It has been a profound infl uence on mathematics, logic, and philosophy, and it covers formal ground and philosophical perspectives beyond the scope of Whitehead and Russell's 'Principia Mathematica' and Frege's 'Grundlagen der Arithmetik'. This book is not only essential to any scholar of the history and...