MU06104 Logic and Set Theory

Mathematical Institute in Opava
Summer 2022
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
doc. RNDr. Michal Marvan, CSc. (lecturer)
Mgr. Jakub Šotola (seminar tutor)
Guaranteed by
prof. RNDr. Jaroslav Smítal, DrSc.
Mathematical Institute in Opava
Prerequisites (in Czech)
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.
  • - 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).
    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
Further comments (probably available only in Czech)
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.
ActivityDifficulty [h]
The course is also listed under the following terms Summer 1998, Summer 1999, Summer 2000, Summer 2001, Summer 2002, Summer 2003, Summer 2004, Summer 2005, Summer 2006, Summer 2007, Summer 2008, Summer 2009, Summer 2010, Summer 2011, Summer 2012, Summer 2013, Summer 2014, Summer 2015, Summer 2016, Summer 2017, Summer 2018, Summer 2019, Summer 2020, Summer 2021.
  • Enrolment Statistics (Summer 2022, recent)
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