[FOM] New Book: Ulrich Kohlenbach, Applied Proof Theory

[Ulrich Kohlenbach]

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