Logical Foundations of Proof Complexity

The current draft (posted September 2, 2008) has 439 pages and is mostly complete except for parts of Chapters 9 and 10 and the Appendix. Further editing is intended.

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Preface, Table of Contents, Introduction (.ps) (15 pages)

Book (including index) (.ps) (9 + 439 pages)

CHAPTER TITLES:

Introduction

The Predicate Calculus and the System LK

Peano Arithmetic and its Subsystems

Two-Sorted Logic and Complexity Classes

The Theory V0 and AC0

The Theory V1 and Polynomial Time

Propositional Translations

Theories for Polynomial Time and Beyond

Theories for Small Classes

The Reflection Principle

(Appendix) Computational Models