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Advanced Model Theory - NLTM011

Title:	Pokročilá teorie modelů
Guaranteed by:	Department of Theoretical Computer Science and Mathematical Logic (32-KTIML)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2022
Semester:	summer
E-Credits:	6
Hours per week, examination:	summer s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech, English
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	doc. RNDr. Josef Mlček, CSc.
Class:	DS, algebra, teorie čísel a matematická logika Mat. logika a teorie množin
Classification:	Informatics > Theoretical Computer Science
Is incompatible with:	NMAG407, NAIL017
Is interchangeable with:	NMAG407, NAIL017

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Annotation -

Last update: T_MUUK (31.01.2001)

Basic constructions of models, completeness and compactness, omitting-types theorem, Skolem functions and indiscernibles. Automorphisms. Countable categoricity. Atomic and prime models. Saturated, homogeneous and universal models, big models. Ultraproducts, regular and good ultrafilters, saturativity of ultraproducts, elementary classes. Stable theories, Morley's theorem on uncountable categoricity.

Aim of the course -

Last update: RNDr. Jan Hric (07.06.2019)

To learn fundamentals of model theory

Course completion requirements -

Last update: RNDr. Jan Hric (07.06.2019)

Oral exam

Literature - Czech

Last update: RNDr. Pavel Zakouřil, Ph.D. (05.08.2002)

C.C.Chang, J.H.Keisler: Model theory, NHPC 1973

W. Hodges: Model Theory, Cambridge Univ. Press, 1993

J. Mlček: Nespočetná kategoričnost, studijní text, 1998

Syllabus -

Last update: T_KTI (19.05.2004)

First-order structures and models, the satisfaction, an existence of models. The compactness and

the completeness theorem. Embeddings and diagrams, chains of models, Lindenbaum algebras. Omitting-types theorems.

Countable categoricity. Saturated, homogenouse and universal models. Big models. Minimal and atomic models. Ultraproducts, regular

and good filters. An isomorphisms theorem. Elementary classes. Indiscernibles. Model completeness.

Morley's theorem on Uncountable categoricity. The stability.