[FOM] New Book: Ulrich Kohlenbach, Applied Proof Theory
Ulrich Kohlenbach
kohlenbach at mathematik.tu-darmstadt.de
Sat May 31 17:18:48 EDT 2008
The following book which might be of interest to readers of FOM just appeared:
Ulrich Kohlenbach:
Applied Proof Theory: Proof Interpretations and their Use in Mathematics
Series: Springer Monographs in Mathematics
2008, XX, 536 p., Hardcover
ISBN: 978-3-540-77532-4, 69,95 EUR (+VAT)/ 99 US Dollar
About this book
Ulrich Kohlenbach presents an applied form of proof theory that has led in
recent years to new results in number theory, approximation theory, nonlinear
analysis, geodesic geometry and ergodic theory (among others). This applied
approach is based on logical transformations (so-called proof interpretations)
and concerns the extraction of effective data (such as bounds) from prima facie
ineffective proofs as well as new qualitative results such as independence of
solutions from certain parameters, generalizations of proofs by elimination of
premises.
The book first develops the necessary logical machinery emphasizing novel
forms of Goedel's famous functional (Dialectica) interpretation. It then
establishes general logical metatheorems that connect these techniques with
concrete mathematics. Finally, two extended case studies (one in
approximation theory and one in fixed point theory) show in detail how this
machinery can be applied to concrete proofs in different areas of mathematics.
Written for:
Researchers and graduate students in the fields of mathematics, computer
science, philosophy of mathematics, and foundations of mathematics
Keywords:
Computational Mathematics
Mathematical logic
Proof Interpretations
Proof Mining
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