MU:MU06104 Logic and Set Theory - Course Information

MU06104 Logic and Set Theory

Mathematical Institute in Opava
Summer 2023

Extent and Intensity

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

Teacher(s)

doc. RNDr. Michal Marvan, CSc. (lecturer)

Guaranteed by

Timetable

Thu 13:55–15:30 115

MU06104/01: Mon 11:25–13:00 RZ, M. Marvan

Prerequisites (in Czech)

TYP_STUDIA(BN)

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

The aim of this subject is to acquaint students with basic concepts of mathematical logic and with the axiomatic set theory.

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

required literature

P. Komjáth, V. Totik. Problems and Theorems in Classical Set Theory. Springer, 2006. info
T. Šalát, J. Smítal. Teória množín. Bratislava, 1995. ISBN 80-223-0974-5. info

recommended literature

P. J. Cameron. Sets, Logic and Categories. Springer, 2005. 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

English

Further comments (probably available only in Czech)

Study Materials
The course can also be completed outside the examination period.

Teacher's information

The examination consists of an oral part.
Requirements for pre-exam credits is a sufficient attendace at the seminars.