This book verifies with compelling evidence the author’s inclination to ‘write a book on proof theory which needs no previous knowledge of proof theory’. Avoiding the cryptic terminology of proof as far as possible, the book starts at an elementary level and displays the connections between infinitary proof theory and generalized recursion theory, especially the theory of inductive definitions. As a ‘warm up’ the classical analysis of Gentzen is presented in a more modern terminology to proceed with explaining and proving the famous resultby Feferman and Schütte on the limits of predicativity. The author, too, provides an introduction to ordinal arithmetic, introduces the Veblen hierarchy and employs these functions to design an ordinal notation system for the ordinals below Epsilon 0 and Gamma 0, while emphasizing the first step into impredicativity, i.e., the first step beyond Gamma 0. Written by a specialist of the subject. INDICE: 1 Historical Background.- 2 Primitive Recursive Functions and Relations.- 3 Ordinals.- 4 Pure Logic.- 5 Truth Complexities for Pi 1-1-Sentences.- 6 Inductive Definitions.- 7 The Ordinal Analysis for Pean Arithmetic.- 8 Autonomous Ordinals and the Limits of Predicativity.- 9 Ordinal Analysis of the Theory for Inductive Definitions.- 10 Provably Recursive Functions of NT.- 11 Ordinal Analysis for Kripke Platek Set Theory with infinity.- 12 Predicativity Revisited.- 13 Non-Monotone Inductive Definitions.- 14 Epilogue.
- ISBN: 978-3-540-69318-5
- Editorial: Springer
- Encuadernacion: Rústica
- Páginas: 369
- Fecha Publicación: 01/09/2008
- Nº Volúmenes: 1
- Idioma: Inglés