Metamathematics of First-Order Arithmetic Perspectives in Logic Series

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the third publication in the Perspectives in Logic series, is a much-needed monograph on the metamathematics of first-order arithmetic. The authors pay particular attention to subsystems (fragments) of Peano arithmetic and give the reader a deeper understanding of the role of the axiom schema of induction and of the phenomenon of incompleteness. The reader is only assumed to know the basics of mathematical logic, which are reviewed in the preliminaries. Part I develops parts of mathematics and logic in various fragments. Part II is devoted to incompleteness. Finally, Part III studies systems that have the induction schema restricted to bounded formulas (bounded arithmetic).

Introduction; Preliminaries; Part I: 1. Arithmetic as number theory, set theory and logic; 2. Fragments and combinatorics; Part II: 3. Self-reference; 4. Models of fragments of arithmetic; Part III: 5. Bounded arithmetic; Bibliographical remarks and further reading; Bibliography; Index of terms; Index of symbols.

Petr Hájek works in the Institute of Computer Science at the Academy of Sciences of the Czech Republic, Prague.
Pavel Pudlák works in the Mathematical Institute at the Academy of Sciences of the Czech Republic, Prague.