Handbook of Mathematical Logic : Handbook of Mathematical Logic
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
1 online resource (1179 pages)
9780080933641, 0080933645
1049808293
Front Cover
Handbook of Mathematical Logic
Copyright Page
Table of Contents
Foreword
Contributors
Part A: Model Theory
Guide to Part A
A.1. An introduction to first-order logic
A.2. Fundamentals of model theory
A.3. Ultraproducts for algebraists
A.4. Model completeness
A.5. Homogenous sets
A.6. Infinitesimal analysis of curves and surfaces
A.7. Admissible sets and infinitary logic
A.8. Doctrines in categorical logic
Part B: Set Theory
Guide to Part B
B.1. Axioms of set theory
B.2. About the axiom of choice
B.3. Combinatorics. B.4. Forcing, John
B.5. Constructibility
B.6. Martin's Axiom
B.7. Consistency results in topology
Part C: Recursion Theory
Guide to Part C
C.1. Elements of recursion theory
C.2. Unsolvable problems
C.3. Decidable theories
C.4. Degrees of unsolvability: a survey of results
C.5. Ü -recursion theory
C.6. Recursion in higher types
C.7. An introduction to inductive definitions
C.8. Descriptive set theory: Projective sets
Part D: Proof Theory And Constructive Mathematics Guide To Part D
Guide to Part D
D.1. The incompleteness theorems. D.2. Proof theory: Some applications of cut-elimination
D.3. Herbrand's Theorem and Gentzen's notion of a direct proof
D.4. Theories of finite type related to mathematical practice
D.5. Aspects of constructive mathematics
D.6. The logic of topoi
D.7. The type free lambda calculus
D.8. A mathematical incompleteness in Peano Arithmetic
Author Index
Subject Index