Mathematical Logic 2
A.Y. 2018/2019
Learning objectives
The course offers an introduction to model theory, including however selected topics usually not covered by standard treatments (equationally definable categories of algebras, Birkhoff's Theorem, Stone duality.)
Expected learning outcomes
Basic knowledge of model theory. More advanced knowledge of selected topics (equationally definable classes of algebras, Stone duality.)
Lesson period: Second semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
Second semester
Course syllabus
1. Recap. Propositional and predicate logic, completeness theorems.
2. Category of models of first-order theories: examples, problems, motivations.
3. Equationally definable cateogories of algebras. Free algebras. Birkhoff's HSP Theorem.
4. Stone duality. Boolean algebras and compact Hausdorff zero-dimensional spaces. Galois connection, adjunction and duality. Applications. Further dualities and generalisations (hints).
5. Selected topics in model theory. (Ultraproducts. Łoś' Theorem. Compactness through Stone duality. Löwenheim-Skolem Theorem. Further more advanced topics - e.g.: types, Omitting Types Theorem, Morley's Categoricity Theorem, etc. - according to the available time and to the interests of attending students.)
2. Category of models of first-order theories: examples, problems, motivations.
3. Equationally definable cateogories of algebras. Free algebras. Birkhoff's HSP Theorem.
4. Stone duality. Boolean algebras and compact Hausdorff zero-dimensional spaces. Galois connection, adjunction and duality. Applications. Further dualities and generalisations (hints).
5. Selected topics in model theory. (Ultraproducts. Łoś' Theorem. Compactness through Stone duality. Löwenheim-Skolem Theorem. Further more advanced topics - e.g.: types, Omitting Types Theorem, Morley's Categoricity Theorem, etc. - according to the available time and to the interests of attending students.)
Website
Professor(s)
Reception:
By appointment
Dipartimento di Matematica "Federigo Enriques", via Cesare Saldini 50, room 2048