The Annual European Meeting of the Association for Symbolic Logic, generally known as the Logic Colloquium, is the most prestigious annual meeting in the field. Many of the papers presented there are invited surveys of recent developments, and the rest of the papers are chosen to complement the invited talks. This volume includes surveys, tutorials, and selected research papers from the 2004 meeting. Highlights include a tutorial survey of the recent highpoints of universal algebra, written by a leading expert; explorations of foundational questions; and a quartet of model theory papers giving an excellent reflection of current work in model theory, from the most abstract aspect 'abstract elementary classes' to issues around p-adic integration.
0. Introduction; 1. Abstract elementary classes: some answers, more questions John T. Baldwin; 2. On the density of Hausdorff ultrafilters Tomek Bartoszynski and Saharon Shelah; 3. Zero groups and maximal tori Alessandro Berarducci; 4. Constructive set theory with operations A. Cantini and L. Crosilla; 5. Parametrized local zeta functions Raf Cluckers; 6. Colourings of hypergraphs, permutation groups and CSP's Benoit Larose and Lucien Haddad; 7. Congruence, tolerance identities; congruence modularity; shifting principle Paolo Lipparini; 8. Universes in type theory part I - inaccessibles and Mahlo Anton Setzer; 9. Hausdorff dimension and weak truth table reducibility Frank Stephan; 10. Computation and the explanation of intelligent behaviours: ethnologically motivated restart Guglielmo Tamburrini and Edoardo Datteri; 11. Constructible sheaves and definability Ivan Tomasic; 12. An overview of modern universal algebra Ross Willard.