#
MU:MU06104 Logic and Set Theory - Course Information

## MU06104 Logic and Set Theory

**Mathematical Institute in Opava**

Summer 2021

**Extent and Intensity**- 2/2/0. 6 credit(s). Type of Completion: zk (examination).
**Teacher(s)**- doc. RNDr. Michal Marvan, CSc. (lecturer)

Mgr. Jakub Šotola (seminar tutor) **Guaranteed by**- prof. RNDr. Jaroslav Smítal, DrSc.

Mathematical Institute in Opava **Timetable**- Mon 8:55–10:30 115
- Timetable of Seminar Groups:

*J. Šotola* **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**- Mathematical Analysis (programme MU, N1101)
- Mathematical Methods and Modelling (programme MU, Bc-M)
- General Mathematics (programme MU, Bc-M)
- Mathematics (programme MU, B1101)

**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).

- - Logic (zero order logic, Post completeness theorem, first order logic, model theory, Goedel incompleteness theorem)
**Literature****Language of instruction**- Czech
**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 are set out by the tutorial lecturer.Activity Difficulty [h] Cvičení 26 Přednáška 26 **Summary**52

- Enrolment Statistics (recent)

- Permalink: https://is.slu.cz/course/sumu/summer2021/MU06104