2: II- First-order Logic
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- 2.1: Syntax and Semantics
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- 2.1.1: Introduction
- 2.1.2: First-Order Languages
- 2.1.3: Terms and Formulas
- 2.1.4: Unique Readability
- 2.1.5: Main operator of a Formula
- 2.1.6: Subformulas
- 2.1.7: Free Variables and Sentences
- 2.1.8: Substitution
- 2.1.9: Structures for First-order Languages
- 2.1.10: Covered Structures for First-order Languages
- 2.1.11: Satisfaction of a Formula in a Structure
- 2.1.12: Variable Assignments
- 2.1.13: Extensionality
- 2.1.14: Semantic Notions
- 2.1.15: Summary
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- 2.4: The Sequent Calculus
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- 2.4.1: Rules and Derivations
- 2.4.2: Propositional Rules
- 2.4.3: Quantifier Rules
- 2.4.4: Structural Rules
- 2.4.5: Derivations
- 2.4.6: Examples of Derivations
- 2.4.7: Derivations with Quantifiers
- 2.4.8: Proof-Theoretic Notions
- 2.4.9: Derivability and Consistency
- 2.4.10: Derivability and the Propositional Connectives
- 2.4.11: Derivability and the Quantifiers
- 2.4.12: Soundness
- 2.4.13: Derivations with Identity predicate
- 2.4.14: Soundness with Identity predicate
- 2.4.15: Summary
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- 2.5: Natural Deduction
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- 2.5.1: Rules and Derivations
- 2.5.2: Propositional Rules
- 2.5.3: Quantifier Rules
- 2.5.4: Derivations
- 2.5.5: Examples of Derivations
- 2.5.6: Derivations with Quantifiers
- 2.5.7: Proof-Theoretic Notions
- 2.5.8: Derivability and Consistency
- 2.5.9: Derivability and the Propositional Connectives
- 2.5.10: Derivability and the Quantifiers
- 2.5.11: Soundness
- 2.5.12: Derivations with Identity predicate
- 2.5.13: Soundness with Identity predicate
- 2.5.14: Summary
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- 2.6: The Completeness Theorem
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- 2.6.1: Introduction
- 2.6.2: Outline of the Proof
- 2.6.3: Complete Consistent Sets of Sentences
- 2.6.4: Henkin Expansion
- 2.6.5: Lindenbaum’s Lemma
- 2.6.6: Construction of a Model
- 2.6.7: Identity
- 2.6.8: The Completeness Theorem
- 2.6.9: The Compactness Theorem
- 2.6.10: A Direct Proof of the Compactness Theorem
- 2.6.11: The Löwenheim-Skolem Theorem
- 2.6.12: Summary