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.
Author(s): Torkel Franzén
Series: Lecture Notes in Logic 16
Publisher: Cambridge University Press
Year: 2017
Language: English
Pages: 318
Contents......Page 7
Preface......Page 9
1 Introduction......Page 12
2 Arithmetical preliminaries......Page 26
3 Primes and proofs......Page 48
4 The language of arithmetic......Page 64
5 The language of analysis......Page 84
6 Ordinals and inductive definitions......Page 98
7 Formal languages and the definition of truth......Page 116
8 Logic and theories......Page 130
9 Peano Arithmetic and computability......Page 154
10 Elementary and classical analysis......Page 186
11 The recursion theorem and ordinal notations......Page 198
12 The incompleteness theorems......Page 220
13 Iterated consistency......Page 236
14 Iterated reflection......Page 252
15 Iterated iteration and inexhaustibility......Page 276
References......Page 304
Index......Page 308
