Academic Year 2018/2019
- Docente: Piero Plazzi
- Credits: 6
- SSD: MAT/01
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: First cycle degree programme (L) in Mathematics (cod. 8010)
Learning outcomes
See the related section in Italian.
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
See the related section in Italian.
Teaching methods
See the related section in Italian.
Assessment methods
See the related section in Italian.
Teaching tools
See the related section in Italian.
Office hours
See the website of Piero Plazzi