Logic Colloquium 2004
This book contains invited surveys, tutorials and selected research papers from the 2004 Annual European Summer Meeting of the Association for Symbolic Logic held in Torino, Italy, covering recent reflection of the work in the fields of model theory, foundations and universal algebra. More specifically: J. Baldwin surveys recent development in the study of abstract elementary classes and raises a number of interesting questions; T. Bartoszynski and S. Shellah use forcing to prove that density of Hausdorff ultrafilters in Rudin-Keisler order is independent of ZFC; and A. Berarducci presents various results on 0-groups and o-minimal structures. On the foundational note, A. Cantini and L. Corosilla present an interesting extension of constructive set theory, A. Setzer starts a series of papers on a proof of theoretically strong extensions of Martin-Löf type theory and G. Tamburrini with E. Datteri revive Turing's and von Neumann's early ideas on computational modelling of intelligent behaviours. R. Cluckers discusses the theory of parametrized p-adic integrals, B. Larose and L. Haddad investigate algorithmic complexity of strong colouring problems in hypergraphs of permutation groups and P. Lipparni introduces a new tolerance identity for algebras. F. Stephan constructs in an oracle-relative world a set whose weak truth-table degree's Hausdorff-dimension is between ¼ and ½. The short note by I. Tomašić clarifies aspects of invariants of the theory of constructible sheaves and cohomologies, which are definable in the language of rings. The proceedings ends with the R. Willard tutorial introducing some deep contemporary results in universal algebra to non-specialists.