Foundations of Mathematical Logic

✍ Scribed by Haskell B. Curry

• Publisher: Dover Publications
• Year: 2010
• Tongue: English
• Leaves: 420
• Series: Dover Books on Mathematics
• Edition: 2 Revised
• Category: Library

✦ Synopsis

Written by a pioneer of mathematical logic, this comprehensive graduate-level text explores the constructive theory of first-order predicate calculus. It covers formal methods, including algorithms and epitheory, and offers a brief treatment of Markov's approach to algorithms, explains elementary facts about lattices and similar algebraic systems, and more. 1963 edition.

✦ Table of Contents

Preface
Explanation of Conventions
CHAPTER 1. INTRODUCTION
A. The nature of mathematical logic
B. The logical antinomies
C. The nature of mathematics
D. Mathematics and logic
S. Supplementary topics
CHAPTER 2. FORMAL SYSTEMS
A. Preliminaries
B. Theories
C. Systems
D. Special forms of systems
E. Algorithms
S. Supplementary topics
CHAPTER 3. EPITHEORY
A. The nature of epitheory
B. Replacement and monotone relations
C. The theory of definition
D. Variables
S. Supplementary topics
CHAPTER 4. RELATIONAL LOGICAL ALGEBRA
A. Logical algebras in general
B. Lattices
C. Skolem lattices
D. Classical Skolem lattices
S. Supplementary topics
CHAPTER 5. THE THEORY OF IMPLICATION
A. General principles of assertional logical algebra
B. Propositional algebras
C. The systems LA and LC
D. Equivalence of the systems
E. L deducibility
S. Supplementary topics
CHAPTER 6. NEGATION
A. The nature of negation:
B. L systems for negation
C. Other formulations of negation
D. Technique of classical negation
S. Supplementary topics
CHAPTER 7. QUANTIFICATION
A. Formulation
B. Theory of the L*systems
C. Other forms of quantification theory
D. Classical epitheory
S. Supplementary topics
CHAPTER 8. MODALITY
A. Formulation of necessity
B. The L theory of necessity
C. The T and H formulations of necessity
S. Supplementary topics
Bibliography
Index