Logic List Mailing Archive

New book: Kohlenbach, Applied Proof Theory

The following book which might be of interest to the recipients of this
email list 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, List price 69,95 EUR (+local VAT) / 99 US$

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, nonline
ar 
analysis, geodesic geometry and ergodic theory (among others). This applied
 
approach is based on logical transformations (so-called proof interpretatio
ns) 
and concerns the extraction of effective data (such as bounds) from prima f
acie 
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 f
orms 
of Gdel's famous functional ('Dialectica') interpretation. It then estab
lishes 
general logical metatheorems that connect these techniques with concrete 
mathematics. Finally, two extended case studies (one in approximation theor
y 
and one in fixed point theory) show in detail how this machinery can be app
lied 
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