Book:Raymond M. Smullyan/First-Order Logic/Second Edition

Raymond M. Smullyan: First-Order Logic (2nd Edition)

Published $\text {1995}$, Dover

ISBN 978-0486683706

Subject Matter

• Predicate Logic

Contents

Preface to the Dover Edition

Preface to the First Edition

Part $\text {I}$. Propositional Logic from the Viewpoint of Analytic Tableaux

Chapter $\text {I}$. Preliminaries

$\S$ 0. Foreword on Trees

$\S$ 1. Formulas of Propositional Logic

$\S$ 2. Boolean Valuations and Truth Sets

Chapter $\text {II}$. Analytic Tableaux

$\S$ 1. The Method of Tableaux

$\S$ 2. Consistency and Completeness of the System

Chapter $\text {III}$. Compactness

$\S$ 1. Analytic Proofs of the Compactness Theorem

$\S$ 2. Maximal Consistency: Lindenbaum's Construction

$\S$ 3. An Analytic Modification of Lindenbaum's Proof

$\S$ 4. The Compactness Theorem for Deducibility

Part $\text {II}$. First-Order Logic

Chapter $\text {IV}$. First-Order Logic. Preliminaries

$\S$ 1. Formulas of Quantification Theory

$\S$ 2. First-Order Valuations and Models

$\S$ 3. Boolean Valuations vs. First-Order Valuations

Chapter $\text {V}$. First-Order Analytic Tableaux

$\S$ 1. Extension of Our Unified Notation

$\S$ 2. Analytic Tableaux for Quantification Theory

$\S$ 3. The Completeness Theorem

$\S$ 4. The Skolem-Löwenheim and Compactness Theorems for First-Order Logic

Chapter $\text {VI}$. A Unifying Principle

$\S$ 1. Analytic Consistency

$\S$ 2. Further Discussion of Analytic Consistency

$\S$ 3. Analytic Consistency Properties for Finite Sets

Chapter $\text {VII}$. The Fundamental Theorem of Quantification Theory

$\S$ 1. Regular Sets

$\S$ 2. The Fundamental Theorem

$\S$ 3. Analytic Tableaux and Regular Sets

$\S$ 4. The Liberalized Rule $D$

Chapter $\text {VIII}$. Axiom Systems for Quantification Theory

$\S$ 0. Foreword on Axiom Systems

$\S$ 1. The System $Q_1$

$\S$ 2. The Systems $Q_2$, $Q_2^*$

Chapter $\text {IX}$. Magic Sets

$\S$ 1. Magic Sets

$\S$ 2. Applications of Magic Sets

Chapter $\text {X}$. Analytic versus Synthetic Consistency Properties

$\S$ 1. Synthetic Consistency Properties

$\S$ 2. A More Direct Construction

Part $\text {III}$. Further Topics in First-Order Logic

Chapter $\text {XI}$. Gentzen Systems

$\S$ 1. Gentzen Systems for Propositional Logic

$\S$ 2. Block Tableaux and Gentzen Systems for First-Order Logic

Chapter $\text {XII}$. Elimination Theorems

$\S$ 1. Gentzen's Hauptsatz

$\S$ 2. An Abstract Form of the Hauptsatz

$\S$ 3. Some Applications of the Hauptsatz

Chapter $\text {XIII}$. Prenex Tableaux

$\S$ 1. Prenex Formulas

$\S$ 2. Prenex Tableaux

Chapter $\text {XIV}$. More on Gentzen Systems

$\S$ 1. Gentzen's Extended Hauptsatz

$\S$ 2. A New Form of the Extended Hauptsatz

$\S$ 3. Symmetric Gentzen Systems

Chapter $\text {XV}$. Craig's Interpolation Lemma and Beth's Definability Theorem

$\S$ 1. Craig's Interpolation Lemma

$\S$ 2. Beth's Definability Theorem

Chapter $\text {XVI}$. Symmetric Completeness Theorems

$\S$ 1. Clashing Tableaux

$\S$ 2. Clashing Prenex Tableaux

$\S$ 3. A Symmetric Form of the Fundamental Theorem

Chapter $\text {XVII}$. Systems of Linear Reasoning

$\S$ 1. Configurations

$\S$ 2. Linear Reasoning

$\S$ 3. Linear Reasoning for Prenex Formulas

$\S$ 4. A System Based on the Strong Symmetric Form of the Fundamental Theorem

References

Subject Index

Further Editions

• 1958: Raymond M. Smullyan: First-Order Logic