- 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. Predicate calculus. 1.1 Alphabet, variables, quantifiers;
wffs, bound or free variables, sentences. Semantics:
interpretations, satisfiability, truth, logical validity.
Models.
1.2 Sentences and propositional logic: truth tables,
tautologies, normal forms and connectives per se.
1.3 Derivation rules, theories, axioms and theorems. Model theorem. Correctness and (Gödel) completeness theorem; compactness and nonstandard models (hints).
2. Two basic mathematical theories. Formal arithmetics
(Peano Arithmetics, or PA) vs classical Peano axioms: basic
recursion theory and Gödel incompleteness theorems for PA (hints).
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