The Operational Perspective
نویسنده
چکیده
For Gerhard Jäger, in honor of his 60 th birthday. Let me begin with a few personal words of appreciation, since Gerhard Jäger is one of my most valued friends and long time collaborators. It's my pleasure to add my tribute to him for his outstanding achievements and leadership over the years, and most of all for having such a wonderful open spirit and being such a fine person. I first met Gerhard at the 1978 logic colloquium meeting in Mons, Belgium. He was attending that with Wolfram Pohlers and Wilfried Buchholz, with both of whom I had long enjoyed a stimulating working relationship on theories of iterated inductive definitions. From our casual conversations there, it was clear that Gerhard was already someone with great promise in proof theory. But things really took off between us a year later when we both visited Oxford University for the academic year 1979-1980. Gerhard had just finished his doctoral dissertation with Kurt Schütte and Wolfram Pohlers. I remember that we did a lot of walking and talking together, though I had to walk twice as fast to keep up with him. We talked a lot about proof theory and in particular about my explicit mathematics program that I had introduced in 1975 and had expanded on in my Mons lectures; Gerhard was quick to take up all my questions and to deal with them effectively. Since then, as hardly needs saying, he became a leader in the development of the proof theory of systems of explicit mathematics and related systems in the applicative/operational framework (among many contributions to a number of other areas), and he went on to establish in Bern a world center for studies in these subjects. It was also through Gerhard that I was able to come in useful contact with a number of his students and members of his group, and most particularly with Thomas Strahm, who then became a second very important collaborator of mine, both on explicit mathematics and the unfolding program, of which I'll say something below. Since some time now, Gerhard and Thomas have been working with me on a book on the foundations 2 of explicit mathematics, and in the last few years we have made great progress on that with the assistance of my former student Ulrik Buchholtz, for which I'm very grateful. 1 Finally on the personal front I want to add …
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