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MSTR Elective 2 - NMAG499

Title:	Výběrová přednáška z MSTR 2
Guaranteed by:	Department of Algebra (32-KA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2023
Semester:	summer
E-Credits:	3
Hours per week, examination:	summer s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	English, Czech
Teaching methods:	full-time
Teaching methods:	full-time
Additional information:	https://users.math.cas.cz/~jerabek/teaching/decidable.html
Note:	you can enroll for the course repeatedly

Guarantor:	Mgr. et Mgr. Emil Jeřábek, Dr., Ph.D.
Class:	M Mgr. MSTR M Mgr. MSTR > Volitelné
Classification:	Mathematics > Algebra

Opinion survey results Examination dates SS schedule Noticeboard

Annotation -

Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (23.12.2023)

Non-repeated universal elective course. In 2023/24: Decidable theories. We will study basic methods for proving algorithmic decidability of first-order theories and main examples of decidable theories.

Course completion requirements

Last update: Mgr. et Mgr. Emil Jeřábek, Dr., Ph.D. (27.12.2023)

Oral exam.

Literature -

Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (23.12.2023)

Wilfrid Hodges: Model Theory, Cambridge University Press, 1993.

Michael O. Rabin: Decidable theories, in: Handbook of Mathematical Logic, 1977, pp. 595-629.

Requirements to the exam -

Last update: Mgr. et Mgr. Emil Jeřábek, Dr., Ph.D. (03.01.2024)

Oral exam to assess understanding of the main results presented during the course.

Syllabus -

Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (23.12.2023)

We will study basic methods for proving algorithmic decidability of first-order theories and main examples of decidable theories.

Tools:

quantifier elimination

interpretations

Ehrenfeucht-Fraïssé games

Mostowski and Feferman-Vaught theorems

Fraïssé limits

Exhibits (depending on time constraints):

theories of abelian groups and modules

ordered abelian groups (divisible, Presburger arithmetic)

algebraically closed and real-closed fields

theories of linear orders

theories of Boolean algebras

theories of random structures

theories of locally free algebras

Skolem arithmetic

Entry requirements -

Last update: Mgr. et Mgr. Emil Jeřábek, Dr., Ph.D. (27.12.2023)

Basic knowledge of mathematical logic and model theory