00662 - Mathematical Logic

Course Unit Page

Academic Year 2018/2019

Learning outcomes

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Course contents

0. Introduction. Mathematical, symbolic, formal logic. Formally correct proofs. Syntax vs semantics.

1. Sentences and propositional logic. Truth tables, formal setting of sentential syntax  (Hilbert-Ackermann axioms, natural deduction) and semantics; tautologies, normal forms and connectives per se.

2.1  Predicate calculus.  Alphabet, variables, quantifiers; wffs, bound or free variables, sentences. Semantics: interpretations, satisfiability, truth, logical validity. Models.

2.2 Derivation rules, theories, axioms and theorems (Hilbert-Ackermann axioms, natural deduction). Model theorem. Correctness and (Gödel) completeness theorem; compactness and nonstandard models (hints).

3. Two basic mathematical theories (hints). 3.1 Formal arithmetics (Peano Arithmetics, or PA) vs classical Peano axioms: basic recursion theory and Gödel incompleteness theorems for PA (hints). 

3.2 Naïve set theory, its "paradoxes" and Zermelo-Fraenkel formal set theory: a comparison.

Readings/Bibliography

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Teaching methods

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Assessment methods

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Teaching tools

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Office hours

See the website of Piero Plazzi