- Docente: Piero Plazzi
- Credits: 6
- SSD: MAT/01
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Mathematics (cod. 8208)
Learning outcomes
Read the related section in Italian.
Course contents
Some knowledge about predicative and propositional logic is
strongly recommmended.
1. Algorithms, arithmetic and Gödel incompleteness
results. Algorithms. Turing machines. Recursivity and
computation of arithmetical functions: primitive recursive
functions, μ-recursivity. Recursive relations, enumerability.
Church-Turing's thesis. Peano Arithmetics. Gödelization and
Gödel's Incompleteness Theorems.
2. Axiomatic set theory. Historical introduction: Cantor's
early theorems on numerical sets, intuitive set theory and
paradoxes (Cantor's and Russel's). The axiomatic approach:
Zermelo-Fraenkel Theory ZF. Ordinal and cardinal numbers:
von Neumann's approach. Some special axioms: Regularity, Choice,
Continuum 'Hypothesis'. Alternative theories: classes and
NBG, nonstandard set theories. Hints on independence
problems.
Fur further details, please read the above section.
Readings/Bibliography
See the related section in Italian. The books by MENDELSON
and HALMOS are translations into Italian from English.
Teaching methods
Read the related section in Italian.
Assessment methods
See the related section in Italian.
Teaching tools
See the related section in Italian.
Links to further information
Office hours
See the website of Piero Plazzi