A compilation of papers presented at the 1999 European Summer Meeting of the Association for Symbolic Logic, Logic Colloquium '99 includes surveys and research articles from some of the world's preeminent logicians. Two long articles are based on tutorials given at the meeting and present accessible expositions of current research in two active areas of logic, geometric model theory and descriptive set theory of group actions. The remaining articles cover current research topics in all areas of mathematical logic, including logic in computer science, proof theory, set theory, model theory, computability theory, and philosophy.

This Festschrift is dedicated to Jan Willem Klop on the occasion of his 60th birthdayon December 19,2005.Its focus is on the lambda calculus, term rewr- ing and process algebra, the ?elds where Jan Willem has made fundamental contributions. Without attempting to give a balanced account of Jan Willem's scienti?c achievements, we recall three accomplishments from the early years of his career that especially stand out. The ?rst is his counterexample showing that the extension of the lambda calculus with surjective pairing lacks the Church-Rosserproperty, or, in modern terminology, is not con?uent 7,9]. This settled a famous open problem, which had challenged several researchers in the lambda calculus community for years. The secondis his pioneeringworkintermrewriting.In hisPhDthesis 9], Jan Willem gave a systematic study of orthogonal rewriting in the general setting of combinatoryreductionsystems(CRSs), therebyputtingtheareasofhigher-order rewriting and orthogonality ?rmly on the map. Some of the ideas in the thesis trace back to the famous Blue Preprint 2], from the period that Jan Willem and some other students were graduating in mathematics and logic, under the supervision of Dirk van Dalen and Henk Barendregt. The third feat is the creation, together with Jan Bergstra 23], of the algebra of communicating processes (ACP). With his early work, Jan Willem provided inspiration for many years of fru- ful research, continuing to this day. For decades he has been a creative and stimulating force in the areas of term rewriting and process algebra. Some of his recent interests are in?nitary rewriting, graph rewriting and the geometry of processes.

This volume contains the proceedings of the 15th International Conference on Rewriting Techniques and Applications (RTA 2004), which was held June 2- 5, 2004, at the RWTH Aachen in Germany. RTA is the major forum for the presentation of research on all aspects of rewriting. Previous RTA conferences took place in Dijon (1985), Bordeaux (1987), Chapel Hill (1989), Como (1991), Montreal (1993), Kaiserslautern (1995), Rutgers (1996), Sitges (1997), Tsukuba (1998), Trento (1999), Norwich (2000), Utrecht (2001), Copenhagen (2002), and Valencia (2003). The program committee selected 19 papers for presentation, including ?ve system descriptions, from a total of 43 submissions. In addition, there were invited talks by Neil Jones, Aart Middeldorp, and Robin Milner. Many people helped to make RTA 2004 a success. I am grateful to the m- bers of the program committee and the external referees for reviewing the s- missionsandmaintainingthehighstandardsoftheRTAconferences. Itisagreat pleasure to thank the conference chair Jurgen ] Giesl and the other members of the local organizing committee. They were in charge of the local organization of all events partaking in the Federated Conference on Rewriting, Deduction, and Programming (RDP). Apart from RTA 2004, these events were: - 2nd International Workshop on Higher-Order Rewriting (Delia Kesner, Femke van Raamsdonk, and Joe Wells), - 5th International Workshop on Rule-Based Programming (Slim Abdennadher and Christophe Ringeissen), - 13thInternationalWorkshoponFunctionaland(Constraint)LogicProgr- ming (Herbert Kuchen), - IFIP Working Group 1."

A compilation of papers presented at the 1999 European Summer Meeting of the Association for Symbolic Logic, Logic Colloquium '99 includes surveys and research articles from some of the world's preeminent logicians. Two long articles are based on tutorials given at the meeting and present accessible expositions of current research in two active areas of logic, geometric model theory and descriptive set theory of group actions. The remaining articles cover current research topics in all areas of mathematical logic, including logic in computer science, proof theory, set theory, model theory, computability theory, and philosophy.