Applied Proof Theory: Proof Interpretations and their Use in Mathematics

I mentioned this book in a recent discussion, but I think it might interest members not following that discussion.

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 Gödel'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.

The site includes some sample pages for your reading pleasure. Not ten lines into the preface does Dana Scott appear, and he is clearly one of us...

Read the preface and share your thoughts!

Comment viewing options

Select your preferred way to display the comments and click "Save settings" to activate your changes.

Looks compelling

I had, in fact, not heard of Ulrich Kohlenbach, so proof theory is not as small a world as it is sometimes supposed... The book looks very attractive, and indeed a must buy.

Some further links:

I knew you would be

I knew you would be interested... But is no one else?

I'm very interested...

...just not competent to comment. :-)