Course: Logic and Set Theory

» List of faculties » MU » MU
Course title Logic and Set Theory
Course code MU/06104
Organizational form of instruction Lecture + Lesson
Level of course Master
Year of study not specified
Semester Summer
Number of ECTS credits 6
Language of instruction Czech, English
Status of course Compulsory, Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Course availability The course is available to visiting students
Lecturer(s)
  • SMÍTAL Jaroslav, prof. RNDr. DrSc.
  • ROTH Samuel Joshua, Mgr. Ph.D.
Course content
- 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).

Learning activities and teaching methods
unspecified
Recommended literature
  • B. Balcar, P. Štěpánek. Teorie množin. Praha, 1986.
  • J. Kolář, O. Štěpánková, M. Chytil. Logika, algebry a grafy. Praha, 1989.
  • T. Šalát, J. Smítal. Teória množín. Bratislava, 1995. ISBN 80-223-0974-5.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Mathematical Institute in Opava Mathematics (2014-IVT) Mathematics courses 3 Summer
Mathematical Institute in Opava Mathematics (2014-F) Mathematics courses 3 Summer
Mathematical Institute in Opava Mathematics (2-F) Mathematics courses 3 Summer
Mathematical Institute in Opava Mathematics (1-IVT) Mathematics courses 3 Summer
Mathematical Institute in Opava Mathematical Analysis (1-IVT) Mathematics courses 4 Summer
Mathematical Institute in Opava Mathematical Analysis (1) Mathematics courses 1 Summer