6.1 Definable Sets and Functions
Definition of definable sets and functions in first order structures, with parameters, examples, closure properties, and proofs.
Tag
First-Order Logic
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5.1 Compactness Theorem
Detailed development of the compactness theorem, its proof via completeness, and fundamental applications in model theory.
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 Quantifiers and Scope
Universal and existential quantifiers, scope, free variables, bound variables, and variable capture.
2.1 Terms, Predicates, Formulas
Syntax of first order logic including terms, predicate symbols, and the formation of formulas.
Chapter 2. First-Order Logic
Extension of propositional logic with terms, predicates, quantifiers, structures, satisfaction, models, validity, and entailment.