Book:Raymond M. Smullyan/First-Order Logic

Raymond M. Smullyan: First-Order Logic
First published 1968, Springer-Verlag.

The first edition is Band 43 of the Ergebnisse der Mathematik und ihrer Grensgebiete series.


 * First edition: 1968, Springer-Verlag, ISBN 978-0387040998, ISBN 978-3540040996
 * Dover edition: 1995, Dover, ISBN 978-0486683706

Subject Matter

 * Predicate Logic

Contents (Dover Edition)
Part I. Propositional Logic from the Viewpoint of Analytic Tableaux
 * Chapter I. Preliminaries
 * $\S$ 0. Foreword on Trees
 * $\S$ 1. Formulas of Propositional Logic
 * $\S$ 2. Boolean Valuations and Truth Sets
 * Chapter II. Analytic Tableaux
 * $\S$ 1. The Method of Tableaux
 * $\S$ 2. Consistency and Completeness of the System
 * Chapter 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 II. First-Order Logic'''
 * Chapter 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 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 VI. A Unifying Principle
 * $\S$ 1. Analytic Consistency
 * $\S$ 2. Further Discussion of Analytic Consistency
 * $\S$ 3. Analytic Consistency Properties for Finite Sets
 * Chapter 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 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 IX. Magic Sets
 * $\S$ 1. Magic Sets
 * $\S$ 2. Applications of Magic Sets
 * Chapter X. Analytic versus Synthetic Consistency Properties
 * $\S$ 1. Synthetic Consistency Properties
 * $\S$ 2. A More Direct Construction

'''Part III. Further Topics in First-Order Logic'''
 * Chapter XI. Gentzen Systems
 * $\S$ 1. Gentzen Systems for Propositional Logic
 * $\S$ 2. Block Tableaux and Gentzen Systems for First-Order Logic
 * Chapter XII. Elimination Theorems
 * $\S$ 1. Gentzen's Hauptsatz
 * $\S$ 2. An Abstract Form of the Hauptsatz
 * $\S$ 3. Some Applications of the Hauptsatz
 * Chapter XIII. Prenex Tableaux
 * $\S$ 1. Prenex Formulas
 * $\S$ 2. Prenex Tableaux
 * Chapter 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 XV. Craig's Interpolation Lemma and Beth's Definability Theorem
 * $\S$ 1. Craig's Interpolation Lemma
 * $\S$ 2. Beth's Definability Theorem
 * Chapter XVI. Symmetric Completeness Theorems
 * $\S$ 1. Clashing Tableaux
 * $\S$ 2. Clashing Prenex Tableaux
 * $\S$ 3. A Symmetric Form of the Fundamental Theorem
 * Chapter 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