Introduction to Proof Theory
by Gilles Dowek
Publisher: ESSLLI 2001
Number of pages: 82
These are the course notes for the 13th European Summer School in Logic, Language and Information. Contents: Predicate Logic; Extension of Predicate Logic; Type Theory; Cut Elimination in Predicate Logic; Cut Elimination in Predicate Logic Modulo.
Home page url
Download or read it online for free here:
by J. Girard, Y. Lafont, P. Taylor - Cambridge University Press
This little book comes from a short graduate course on typed lambda-calculus given at the Universite Paris. It is not intended to be encyclopedic and the selection of topics was really quite haphazard. Some very basic knowledge of logic is needed.
by Jon Barwise, John Etchemendy - Center for the Study of Language
The book covers the boolean connectives, formal proof techniques, quantifiers, basic set theory, induction, proofs of soundness and completeness for propositional and predicate logic, and an accessible sketch of Godel's first incompleteness theorem.
by Greg Restall - consequently.org
A textbook in philosophical logic, accessible to someone who's done only an intro course in logic, covering some model theory and proof theory of propositional logic, and predicate logic. User-friendly and philosophically motivated presentation.
by M. Randall Holmes - Boise State University
This textbook is intended to communicate something about proof, sets, and logic. It is about the foundations of mathematics, a subject which results when mathematicians examine the subject matter and the practice of their own subject very carefully.