The handbook is divided into four parts: model theory, set theory, recursion theory and proof theory. Each of the four parts begins with a short guide to the chapters that follow. Each chapter is written for non-specialists in the field in question. Mathematicians will find that this book provides them with a unique opportunity to apprise themselves of developments in areas other than their own.
Author(s): Jon Barwise (ed.)
Series: Studies in Logic and the Foundations of Mathematics 90
Publisher: Elsevier, Academic Press
Year: 1999
Language: English
Pages: 1179
Front Cover......Page 1
Handbook of Mathematical Logic......Page 4
Copyright Page......Page 5
Table of Contents......Page 11
Foreword......Page 8
Contributors......Page 9
Part A: Model Theory......Page 14
Guide to Part A......Page 16
A.1. An introduction to first-order logic......Page 18
A.2. Fundamentals of model theory......Page 60
A.3. Ultraproducts for algebraists......Page 118
A.4. Model completeness......Page 152
A.5. Homogenous sets......Page 194
A.6. Infinitesimal analysis of curves and surfaces......Page 210
A.7. Admissible sets and infinitary logic......Page 246
A.8. Doctrines in categorical logic......Page 296
Part B: Set Theory......Page 328
Guide to Part B......Page 330
B.1. Axioms of set theory......Page 334
B.2. About the axiom of choice......Page 358
B.3. Combinatorics......Page 384
B.4. Forcing, John......Page 416
B.5. Constructibility......Page 466
B.6. Martin’s Axiom......Page 504
B.7. Consistency results in topology......Page 516
Part C: Recursion Theory......Page 536
Guide to Part C......Page 538
C.1. Elements of recursion theory......Page 540
C.2. Unsolvable problems......Page 580
C.3. Decidable theories......Page 608
C.4. Degrees of unsolvability: a survey of results......Page 644
C.5. α -recursion theory......Page 666
C.6. Recursion in higher types......Page 694
C.7. An introduction to inductive definitions......Page 752
C.8. Descriptive set theory: Projective sets......Page 796
Part D: Proof Theory And Constructive Mathematics Guide To Part D......Page 830
Guide to Part D......Page 832
D.1. The incompleteness theorems......Page 834
D.2. Proof theory: Some applications of cut-elimination......Page 880
D.3. Herbrand’s Theorem and Gentzen’s notion of a direct proof......Page 910
D.4. Theories of finite type related to mathematical practice......Page 926
D.5. Aspects of constructive mathematics......Page 986
D.6. The logic of topoi......Page 1066
D.7. The type free lambda calculus......Page 1104
D.8. A mathematical incompleteness in Peano Arithmetic......Page 1146
Author Index......Page 1156
Subject Index......Page 1164
