. – Mathematical Logic PROFESSOR ANTONINO VENTURA Text under revision. Not yet approved by academic staff. COURSE AIMS Construction of a formal language and its use in propositional and predicate logic. COURSE CONTENT 1. FORMAL LANGUAGE OF DEDUCTION. - Nature, purpose and role of logic. Notion of proposition. Simple and complex propositions. Structure of a proposition. Propositional connectives. Quantifiers. Determination of the truth value of complex propositions. Definition of certain connectives by means of others. Formal language in the construction of a calculation. 2. PROPOSITIONAL LOGIC. - 3. Syntax of classical propositional logic. Rudiments of intuitionistic and minimal calculus. Truth of a formula in an interpretation. Notions of satisfiability, logical consequence and validity. Semantics of classical propositional logic. Correctness theorem, completeness theorem and finiteness theorem (compactness) for classic propositional calculus. PREDICATE LOGIC. - Syntax of predicate logic. Fundamental semantic notions. Semantics of first order predicate logic. Correctness theorem and completeness theorem for predicate calculus. Consequences of semantic completeness. Finiteness as a presupposition for formality. The problem of axiomatization of theories. Non-categoricity of elementary arithmetic (Skolem's Theorem) and categoricity of second-order Peano arithmetic (Dedekind's theorem). READING LIST S. GALVAN, Logica, La Scuola, Brescia, 2012. E. J. LEMMON, Elementi di logica, Laterza, Roma-Bari 2009. E. MENDELSON, Introduzione alla logica matematica, Bollati Boringhieri, Turin, 1972. G. LOLLI, Introduzione alla logica formale, Il Mulino, Bologna, 1991. Other books will be recommended during the course. TEACHING METHOD Lectures. ASSESSMENT METHOD Oral examinations. NOTES Further information can be found on the lecturer's webpage http://www2.unicatt.it/unicattolica/docenti/index.html or on the Faculty notice board. at

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# Mathematical Logic