- Docente: Piero Plazzi
- Credits: 6
- SSD: MAT/01
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
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Corso:
Second cycle degree programme (LM) in
Mathematics (cod. 5827)
Also valid for Second cycle degree programme (LM) in Mathematics (cod. 8208)
Learning outcomes
Please see 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 italian section.
Readings/Bibliography
See the related section in Italian. The books by MENDELSON and HALMOS are translations into Italian from English: the latter edition is available in Department library.
Teaching methods
Read the related section in Italian.
Assessment methods
See the related section in Italian.
Teaching tools
Read the related section in Italian.
Office hours
See the website of Piero Plazzi