Inexhaustibility

A Non-Exhaustive Treatment

Torkel Franzén

• Publisher: Cambridge University Press
• Topic: Mathematics
• eBook ISBN:
  9781108641630
• Subtopic: Logic in Mathematics
• Index: Mathematics

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 sixteenth publication in the Lecture Notes in Logic series, gives a sustained presentation of a particular view of the topic of Gödelian extensions of theories. It presents the basic material in predicate logic, set theory and recursion theory, leading to a proof of Gödel's incompleteness theorems. The inexhaustibility of mathematics is treated based on the concept of transfinite progressions of theories as conceived by Turing and Feferman. All concepts and results are introduced as needed, making the presentation self-contained and thorough. Philosophers, mathematicians and others will find the book helpful in acquiring a basic grasp of the philosophical and logical results and issues.

Table of contents

• Cover
• Half-title
• Series information
• Title page
• Copyright information
• Dedication
• Table of contents
• Preface
• 1 Introduction
• 2 Arithmetical preliminaries
• 3 Primes and proofs
• 4 The language of arithmetic
• 5 The language of analysis
• 6 Ordinals and inductive definitions
• 7 Formal languages and the definition of truth
• 8 Logic and theories
• 9 Peano Arithmetic and computability
• 10 Elementary and classical analysis
• 11 The recursion theorem and ordinal notations
• 12 The incompleteness theorems
• 13 Iterated consistency
• 14 Iterated reflection
• 15 Iterated iteration and inexhaustibility
• References
• Index