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| Preface | |
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| Note to the Student | |
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| The Propositional Calculus | |
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| Formation Rules for P | |
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| Formal Semantics of P | |
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| Axiomatization of P | |
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| The Deduction Theorem | |
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| Some Theorem Schemas of P | |
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| Completeness | |
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| First-Order Logic | |
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| Formation Rules for L([characters not reproducible], X) | |
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| Free and Bound Variables | |
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| Models | |
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| Validity | |
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| Axiomatization of L([characters not reproducible], X) | |
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| Propositional Calculus | |
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| The Deduction Theorem | |
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| Some Theorems of First-Order Logic | |
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| The Soundness Theorem | |
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| The Extension Lemma | |
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| The Completeness Theorem | |
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| First-Order Logic with Equality | |
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| First-Order Recursive Arithmetic | |
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| Primitive Recursive Functions | |
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| Some Primitive Recursive Functions | |
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| Formation Rules for RA | |
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| Semantics | |
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| Axiomatics | |
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| Soundness | |
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| Sentences without Variables | |
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| Arithmetization of Syntax | |
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| Finite Sums and Products | |
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| Primitive Recursive Relations | |
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| Definition by Cases and the Least Number Operator | |
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| Prime Numbers | |
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| Primitive Recursiveness of the Prime Decomposition | |
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| Godel Numbers | |
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| Primitive Recursiveness of the Notion of Function Constant | |
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| Primitive Recursiveness of the Notion of Term | |
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| Primitive Recursiveness of the Notion of Wff | |
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| Substitution | |
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| Deductions | |
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| The Incompleteness Theorems and Other Applications of the Liar Paradox | |
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| The First Godel Incompleteness Theorem | |
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| Proof of the First Godel Theorem in RA | |
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| The Second Godel Incompleteness Theorem | |
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| Tarski's Theorem | |
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| Arithmetical Sets | |
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| Recursive Sets and Decision Procedures | |
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| Church's Theorem for RA | |
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| Second-Order Logic | |
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| Formation Rules for L[subscript 2]([characters not reproducible], X) | |
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| Axiomatics for L[subscript 2]([characters not reproducible], X) | |
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| Semantics of Second-Order Logic | |
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| The Completeness Theorem for Second-Order Logic | |
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| Equality | |
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| Second-Order Peano Arithmetic | |
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| Primitive Recursive Functions | |
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| Numeralwise Representability | |
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| Godel's Theorem for PA[subscript 2] | |
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| Church's Theorem for Second-Order Logic | |
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| Categoricity of PA[subscript 2] | |
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| Skolem's Paradox | |
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| Formal Set Theory | |
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| Appendix | |
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| Sets and Functions | |
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| Induction | |
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| Primitive Recursion | |
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| Countable Sets | |
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| Answers to Selected Exercises | |
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| Suggested Reading | |
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| Index of Symbols | |
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| Index | |