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| Preface | |
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| The Elements | |
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| Introduction | |
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| Extensionality | |
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| Sets | |
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| Mathematical Proof | |
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| Relations | |
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| Some Binary Relations | |
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| Equivalence Relations | |
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| Orderings | |
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| Functions | |
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| Numbers | |
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| Propositional Logic | |
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| Introduction | |
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| Induction and Formal Languages | |
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| Syntax | |
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| Semantics | |
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| Unique Readability | |
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| Recursive Definitions | |
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| Expressive Completeness | |
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| Expressively Complete Languages | |
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| First-Order Logic: Syntax and Semantics | |
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| Introduction | |
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| Properties, Relations and Individuals | |
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| Truth-Functional Composition | |
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| Functions | |
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| Identity | |
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| Quantification | |
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| Syntax | |
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| Semantics | |
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| Truth | |
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| Logical Consequence and Other Logical Notions | |
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| Models | |
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| Equivalence Relations | |
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| Orderings | |
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| Structures for the First-Order Language with No Extralogical Symbols | |
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| Groups | |
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| Arithmetic | |
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| Deduction | |
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| Introduction | |
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| The Basic Rule and the Connective Rules | |
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| Propositional Deduction | |
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| Substitution | |
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| Quantifier and Identity Rules | |
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| Establishing (First-Order) Deducibility Claims | |
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| The Definition of Deducibility | |
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| Deducibility in Different Languages | |
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| Soundness and Completeness | |
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| Soundness | |
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| Completeness, Consistency and Model Existence | |
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| Canonical Structures and Well-Rounded Sets, I: First-Order Languages without Identity | |
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| Canonical Structures and Well-Rounded Sets, II: First-Order Languages with Identity | |
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| A Well-Rounded Set of Sentences Is the Theory of its Canonical Structure | |
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| Negation Completeness | |
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| Henkin Constants and Henkin Axioms | |
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| Consistent, Negation-Complete Henkin Sets Are Well Rounded | |
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| Compactness | |
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| Cardinality | |
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| The Size of Infinity | |
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| Criteria for Size Claims | |
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| Counting | |
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| Functional Criteria | |
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| Same Size | |
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| Big and Small | |
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| Addition | |
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| Multiplication | |
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| Exponentiation | |
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| Cardinality | |
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| Contextual Definition | |
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| Continuities | |
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| Denumerable Sets | |
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| Diagonals | |
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| ZF | |
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| Choice | |
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| Zorn's Lemma | |
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| Completeness for Uncountable Languages | |
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| Expressive Limitations | |
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| Representation and Indiscernibility | |
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| Isomorphic Structures | |
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| Isomorphic Structures and Contextual Definitions | |
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| Representing Finite Structures | |
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| The Downward Lowenheim-Skolem Theorem | |
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| Skolem's Paradox | |
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| The Upward Lowenheim-Skolem Theorem | |
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| Finite Structures Again | |
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| Nonstandard Models of Arithmetic | |
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| Strict Dense Linear Orderings with no Minimal or Maximal Elements | |
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| Categoricity in Power | |
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| Decidability | |
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| Decidable Sets of Sentences and Indiscernible Structures | |
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| Vaught's Test | |
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| Strict Dense Linear Orderings with No Minimal or Maximal Elements | |
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| Successor Arithmetic | |
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| Quantifier Elimination | |
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| Strict Dense Linear Orderings with No Minimal or Maximal Elements | |
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| Successor Arithmetic | |
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| Ordered Successor Arithmetic | |
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| The Decision Problem | |
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| Decidable Structures | |
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| Godel's First Incompleteness Theorem | |
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| Set Theory Revisited | |
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| Symbols and Notation | |
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| Greek Letters | |
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| Index | |