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

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

Published $1995$, Dover

ISBN 978-0486683706.

Subject Matter


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
Subject Index