Propositional Calculus: the notion of formal language. Formal language of propositional calculus. Translations. Inductive definitions and recursive definitions. The semantics of propositional language. The notion of logical consequence. Algebra of propositions. The Natural Deduction system for Classical logic. Calculation of Predicates: the formal language of calculating first order predicates. Semantics for first order language. Definability, homomorphisms between structures. The Natural Deduction system for classical First Order logic.
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