Page 11 - Textos de Matemática Vol. 40

Preface
This work was accepted as Habilitationsschrift by the Fakult¨at fu¨r Informations- und Kognitionswissenschaften of the Eberhard Karls Universit¨at Tu¨bingen in July 2007.
I like to thank my colleagues Andrea Cantini, from Florence, Gerhard Ja¨ger, Thomas Strahm, and Thomas Studer, all from Berne, for the scien- tific discussions and collaborations from which this Habilitationsschrift results. I also have to thank a long list of colleagues and friends with who I was working together all along and which contributed in one or the other way to the work presented here. I apologize that I cannot mention all of them here by name—a given list would probably be incomplete in any case. But I would like to men- tion at least Peter Schroeder-Heister, Tu¨bingen, who introduced me to the academic world beyond the aspect of research. I also like to mention Ra- jeev Gore`, Canberra, Kerry Ojakian, Lisbon, and Geoff Ostrin, Berne, for improving my English in some of the publications which are incorporated in this thesis. However, the responsibility for the English of the given text is en- tirely mine, and I apologize for possible orthographic, grammatical and stylistic errors. Finally, I am grateful to D. and I. Kahle for a thorough review of the text as well as to I. Oitavem for a lot of helpful comments.
The work presented here was elaborated while I was appointed by the Uni- versity of Tu¨bingen, the Ludwig-Maximilians-University of Munich, the New University of Lisbon, and the University of Coimbra. Part of the research was carried out while visiting Stanford University, USA, the Mittag-Leffler-Institute, Sweden, and—during a Research in Pairs visit—the Mathematical Research Institute in Oberwolfach, Germany. I thank these institutions for their hos- pitality and the research environment they provided. When I started my re- search on applicative theories at the University of Berne, I was supported by the Schweizerische Nationalfonds, later on I received support from the Deutsche Forschungsgemeinschaft, the Portuguese Fundac¸a˜o para a Ciˆencia e a Tecnolo- gia, and CENTRIA, the Center of Artificial Intelligence at the New University of Lisbon, which is gratefully acknowledged. Finally, I thank the Departamento de Matem´atica of the Universidade de Coimbra and the editors for including this Habilitationsschrift in the series Textos de Matem´atica.
In the following we freely make use of the papers [JKS99], [JKS01], [Kah99], ix