First-Order Logic

I. Propositional Logic from the Viewpoint of Analytic Tableaux.- I. Preliminaries.- 0. Foreword on Trees.- 1. Formulas of Propositional Logic.- 2. Boolean Valuations and Truth Sets.- II. Analytic Tableaux.- 1. The Method of Tableaux.- 2. Consistency and Completeness of the System.- III. Compactness.- 1. Analytic Proofs of the Compactness Theorem.- 2. Maximal Consistency: Lindenbaum's Construction.- 3. An Analytic Modification of Lindenbaum's Proof.- 4. The Compactness Theorem for Deducibility.- II. First-Order Logic.- IV. First-Order Logic. Preliminaries.- 1. Formulas of Quantification Theory.- 2. First-Order Valuations and Models.- 3. Boolean Valuations vs. First-Order Valuations.- V. First-Order Analytic Tableaux.- 1. Extension of Our Unified Notation.- 2. Analytic Tableaux for Quantification Theory.- 3. The Completeness Theorem.- 4. The Skolem-Lowenheim and Compactness Theorems for First-Order Logic.- VI. A Unifying Principle.- 1. Analytic Consistency.- 2. Further Discussion of Analytic Consistency.- 3. Analytic Consistency Properties for Finite Sets.- VII. The Fundamental Theorem of Quantification Theory.- 1. Regular Sets.- 2. The Fundamental Theorem.- 3. Analytic Tableaux and Regular Sets.- 4. The Liberalized Rule D.- VIII. Axiom Systems for Quantification Theory.- 0. Foreward on Axiom Systems.- 1. The System Q1.- 2. The Systems Q2, Q*2.- IX. Magic Sets.- 1. Magic Sets.- 2. Applications of Magic Sets.- X. Analytic versus Synthetic Consistency Properties.- 1. Synthetic Consistency Properties.- 2. A More Direct Construction.- III. Further Topics in First-Order Logic.- XI. Gentzen Systems.- 1. Gentzen Systems for Propositional Logic.- 2. Block Tableaux and Gentzen Systems for First-Order Logic.- XII. Elimination Theorems.- 1. Gentzen's Hauptsatz.- 2. An Abstract Form of the Hauptsatz Ill.- 3. Some Applications of the Hauptsatz.- XIII. Prenex Tableaux.- 1. Prenex Formulas.- 2. Prenex Tableaux.- XIV. More on Gentzen Systems.- 1. Gentzen's Extended Hauptsatz.- 2. A New Form of the Extended Hauptsatz.- 3. Symmetric Gentzen Systems.- XV. Craig's Interpolation Lemma and Beth's Definability Theorem.- 1. Craig's Interpolation Lemma.- 2. Beth's Definability Theorem.- XVI. Symmetric Completeness Theorems.- 1. Clashing Tableaux.- 2. Clashing Prenex Tableaux.- 3. A Symmetric Form of the Fundamental Theorem.- XVII. Systems of Linear Reasoning.- 1. Configurations.- 2. Linear Reasoning.- 3. Linear Reasoning for Prenex Formulas.- 4. A System Based on the Strong Symmetrie Form of the Fundamental Theorem.- References.