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Kreiseliana: about and around Georg Kreisel. (English) Zbl 0894.03002

Wellesley, MA: A K Peters. xiii, 495 p. (1996).

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This collections of papers, written on the occasion of Georg Kreisel’s 70th birthday (15. September 1993), brings together contributions with reminiscences (14 papers), on Kreisel’s mathematics (6 papers), on his philosophy (3 papers), and a technical tribute (2 papers).
The reminiscences are given by Henk Barendregt, Jon Barwise, Francis Crick, John N. Crossley, Anita Burdman Feferman, Verena Huber-Dyson, Freeman Dyson, Carl G. Jockusch jun., Michael Morley, Anil Nerode, Rohit Parikh, Richard A. Platek, Gerald E. Sacks, and Gaisi Takeuti. They contain not only insights into life and character of Kreisel, but also interesting autobiographical material on the authors.
Kreisel’s mathematics is treated by Charles N. Delzell (“Kreisel’s unwinding of Artin’s proof”), Solomon Feferman (“Kreisel’s ‘unwinding’ program”), William A. Howard (“Some proof theory in the 1960’s”), Horst Luckhardt (“Bounds extracted by Kreisel from ineffective proofs”), David McCarty (“Completeness for intuitionistic logic”), and Helmut Schwichtenberg (“Density and choice for total continuous functionals”).
Kreisel’s philosophy is discussed by Carlo Cellucci (“Mathematical logic: What has it done for the philosophy of mathematics?”), Piergiorgio Odifreddi (“Kreisel’s Church”), and Paul Weingartner (“Some critical remarks on definitions and on philosophical and logical ideals”).
The authors of the technical tribute are Angus Macintyre and A. J. Wilkie (“On the decidability of the real exponential field”), and Gregory Mints (“Normal forms for sequent derivations”).
Moreover, the volume contains a telegraphic vita of Kreisel and a photograph taken in 1959.
The articles of mathematical interest will be reviewed individually.
Indexed articles:
Barendregt, Henk, Kreisel, lambda calculus, a windmill and a castle, 3-14 [Zbl 0894.01007]
Barwise, Jon, The right things for the right reasons, 15-23 [Zbl 0894.01008]
Crick, Francis, Georg Kreisel: A few personal recollections, 25-32 [Zbl 0894.01010]
Crossley, John N., Kreisel’s effectiveness, 33-41 [Zbl 0894.01011]
Burdman Feferman, Anita, Kreisel on the telephone: An appreciation, 43-49 [Zbl 0894.01009]
Huber-Dyson, Verena, Thoughts on the occasion of Georg Kreisel’s 70th birthday, 51-73 [Zbl 0895.01011]
Dyson, Freeman, Addendum: “Thoughts on the occasion of Georg Kreisel’s 70th birthday”, 75 [Zbl 0894.01012]
Jockusch, Carl G. jun., A letter from Professor Kreisel, 77-78 [Zbl 0894.01013]
Morley, Michael, Two insights, 79-80 [Zbl 0894.01014]
Nerode, Anil, An appreciation of Kreisel, 81-88 [Zbl 0895.01006]
Parikh, Rohit, Some reminiscences of Kreisel, 89-96 [Zbl 0895.01010]
Platek, Richard A., Kreisel, generalized recursion theory, Stanford and me, 97-102 [Zbl 0895.01008]
Sacks, Gerald E., Kreisel, generalized recursion theory and me, 103-106 [Zbl 0895.01007]
Takeuti, Gaisi, Kreisel and I, 107-109 [Zbl 0894.01015]
Delzell, Charles N., Kreisel’s unwinding of Artin’s proof, 113-246 [Zbl 0876.12002]
Feferman, Solomon, Kreisel’s “unwinding” program, 247-273 [Zbl 0889.03045]
Howard, William A., Some proof theory in the 1960’s, 275-288 [Zbl 0881.01013]
Luckhardt, Horst, Bounds extracted by Kreisel from ineffective proofs, 289-300 [Zbl 0896.03005]
McCarty, David, Completeness for intuitionistic logic, 301-334 [Zbl 0896.03007]
Schwichtenberg, Helmut, Density and choice for total continuous functionals, 335-362 [Zbl 0901.03039]
Cellucci, Carlo, Mathematical logic: What has it done for the philosophy of mathematics?, 365-388 [Zbl 0877.03007]
Odifreddi, Piergiorgio, Kreisel’s Church, 389-415 [Zbl 0897.03005]
Weingartner, Paul, Some critical remarks on definitions and on philosophical and logical ideals, 417-438 [Zbl 0897.03006]
Macintyre, Angus; Wilkie, A. J., On the decidability of the real exponential field, 441-467 [Zbl 0896.03012]
Mints, Gregory, Normal forms for sequent derivations, 469-492 [Zbl 0897.03053]

MSC:

03-03 History of mathematical logic and foundations
01A70 Biographies, obituaries, personalia, bibliographies
01A60 History of mathematics in the 20th century
01-02 Research exposition (monographs, survey articles) pertaining to history and biography
03-02 Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations
00B15 Collections of articles of miscellaneous specific interest
03A05 Philosophical and critical aspects of logic and foundations
03F50 Metamathematics of constructive systems

Biographic References:

Kreisel, Georg
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