All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. ISBN 978-3-03719-088-3 The Swiss National Library lists this publication in The Swiss Book, the Swiss national bibliography, and the detailed bibliographic data are available on the Internet at. Author: Jean-Yves Girard CNRS, Institut de Mathématiques de Luminy UMR 6206 163 Avenue de Luminy, Case 907 13288 Marseille cedex 9 France E-mail: Ģ010 Mathematics Subject Classification: 03-01, 03A05, 03B40, 03F(03-05-07-10-20-40-52-99), 18A15, 68Q(05-10-12-15-55) Key words: Logic, proof-theory, incompleteness, sequent calculus, natural deduction, lambda-calculus, Curry–Howard isomorphism, system F, coherent spaces, linear logic, proof-nets, ludics, implicit complexity, geometry of interaction
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