Proof Theory and Logical Complexity

by Jean-Yves Girard

Hardbound. This volume is the first in a series which will, in the future, be published jointly by Bibliopolis, Edizioni di Filosofia e Scienze spa, Napoli, and under the North-Holland imprint by Elsevier Science Publishers, Amsterdam.

This is the first of a two-part work covering the main ideas and techniques of proof theory. This volume is introductory, starting with Hilbert (whose second problem in the famous list of problems of 1900 was the consistency of number theory), describing Hilbert's program and its demise at the hands of Gödel. It then proceeds with Gentzen's result (the Hauptsatz is the main result of Part I) and improvements and generalizations to &ohgr;-logic.

Volume II will cover more advanced logics.

Genres: Logic

503 pages, Hardcover

First published October 1, 1987

About the author

Jean-Yves Girard (born 1947) is a French logician working in proof theory. His contributions include a proof of strong normalization in a system of second-order logic called system F; the invention of linear logic; the geometry of interaction; and ludics. He also invented the mustard watch.

Alumnus of the École normale supérieure de Saint-Cloud, Girard is a research director of CNRS in Marseille and a corresponding member of the French Academy of Sciences.