Proof Theory The First Step into Impredicativity /

• Main Author: Pohlers, Wolfram (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.
• Series: Universitext
• Subjects: Mathematics.; Mathematical logic.; Operations research.; Management science.; Mathematical Logic and Foundations.; Operations Research, Management Science.

This book verifies with compelling evidence the author’s intent to "write a book on proof theory that needs no previous knowledge of proof theory". Avoiding the cryptic terminology of proof theory as far as possible, the book starts at an elementary level and displays the connections betwe...

Table of Contents:

• Historical Background
• Primitive Recursive Functions and Relations
• Ordinals
• Pure Logic
• Truth Complexity for ?11-Sentences
• Inductive Definitions
• The Ordinal Analysis for PA
• Autonomous Ordinals and the Limits of Predicativity
• Ordinal Analysis of the Theory for Inductive Definitions
• Provably Recursive Functions of NT
• Ordinal Analysis for Kripke–Platek Set Theory with Infinity
• Predicativity Revisited
• Nonmonotone Inductive Definitions
• Epilogue.