Preface

Summary

The 2001 European Summer Meeting of the Association for Symbolic Logic, Logic Colloquium 2001 was held at the Vienna University of Technology in Vienna, Austria August 6–11, 2001. It was organized by the International Kurt Godel Society on the occasion of the 70th anniversary of Godel's famous publication Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I.

The program of the Logic Colloquium 2001 included 17 invited one hour plenary addresses, 2 tutorials and 17 invited half-hour lecturers in parallel special sessions on Set Theory, ModelTheory, Proof Theory and Proof Search, Computability Theory, Philosophy and History of Logic, Computer Science and Complexity Theory. In addition, there were 126 contributed talks plus 36 papers presented by title. The number of registered participants was 249 coming from around 25 countries.

The tutorial short courses were given by Alexander Leitsch, Resolution theorem proving, and Itay Neeman, Determinacy of long games.

Invited plenary addresses were given by Toshiyasu Arai, Wellfoundedness proofs in reflecting universes; SteveAwodey,Modal and intensional types in categorical logic; James Cummings, Squares, scales and reflection; RodDowney, Calibrating randomness; Harvey Friedman, Recent incompleteness; Warren Goldfarb, Gödel and Carnap: influence and opposition; Olga Kharlampovich, First order properties of free groups; Julia Knight, Quantifiers and complexity; Michiel van Lambalgen, Moschovakis's notion of meaning as applied to linguistics; Chris Miller, Tameness phenomena in expansions of the field of real numbers; RanRaz, Resolution Lower bounds for the weak pigeonhole principle; Saharon Shelah, (N_n, N₀) may fail N0–compactness; Jouko Vaananen, Models, trees and infinitary back-and-forth; FrankWagner, Simplicity theory; Stan Wainer, Provable recursiveness and complexity.

Special plenary addresses commemorating the anniversary of Godel's incompleteness theorem were given by Georg Kreisel, A consumer's (re)view around higher infinites, and Gaisi Takeuti, Incompleteness theorem and its frontier.

The Programm Committee consisted of M. Arslanov, M. Baaz, W. Buchholz, S. Friedman, D. Isaacson, C. Jockusch, J. Krajíček (Chair), L. Newelski (resigned April 2000), J. Paris, J.-P. Ressayre, L. van den Dries, B. Velickovic, A. Visser.

The editors invited all pleanry, section and tutorial speakers to contribute to the proceedings. The present volume contains 19 papers. All papers were refereed. We appreciated very much the help of the referees (whose names we do not present for obvious reasons).