4.1 Structure vs Instance
Distinguishing abstract structures from their concrete instances, and using that distinction to reason across examples.
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Models
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Chapter 4. Structures and Models
Basic model theoretic notions including languages, signatures, substructures, embeddings, elementary equivalence, isomorphism, and examples.
2.5 Validity and Entailment
Validity, semantic entailment, satisfiability, countermodels, and logical consequence in first order logic.
2.4 Satisfaction and Models
Satisfaction, truth in a structure, models of sentences, and theories in first order logic.
2.3 Structures and Interpretations
Structures, domains, and interpretations of symbols in first order logic.
2.2 Formal Systems and Semantics
Syntax, axioms, inference rules, and the semantic interpretation of mathematical languages.