MU:MU06104 Logic and Set Theory - Course Information

MU06104 Logic and Set Theory

Mathematical Institute in Opava
Summer 2019

Extent and Intensity

2/2/0. 6 credit(s). Type of Completion: zk (examination).

Teacher(s)

Guaranteed by

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

Course objectives (in Czech)

Základy matematické logiky, výrokový počet, predikátový počet. Axiomatická teorie množin, kardinální čísla, ordinální čísla, axiom výběru.

Syllabus

- Logic (zero order logic, Post completeness theorem, first order logic, model theory, Goedel incompleteness theorem)
- Axiomatic construction of set theory (Russel's paradox in naive set theory, language of set theory, basic axioms, infinity axiom and the axiom of choice)
- Cardinal numbers (equivalence of sets, cardinal numbers, cardinal arithmetic, comparison of cardinals, Cantor-Bernstein theorem, Cantor diagonal method, continuum hypothesis)
- Ordinal numbers (well-ordered sets, ordinal arithmetic, comparison of ordinals, Zermelo theorem and its consequences for cardinal numbers, alephs).

Literature

recommended literature

T. Šalát, J. Smítal. Teória množín. Bratislava, 1995. ISBN 80-223-0974-5. info
J. Kolář, O. Štěpánková, M. Chytil. Logika, algebry a grafy. Praha, 1989. info
B. Balcar, P. Štěpánek. Teorie množin. Praha, 1986. info

Language of instruction

Czech

Further comments (probably available only in Czech)

The course can also be completed outside the examination period.