MUC61 Logic foundations of mathematics

Faculty of Science
Autumn 2025
Extent and Intensity
2/0/0. 4 credit(s). Type of Completion: zk (examination).
In-person direct teaching
Teacher(s)
doc. RNDr. Eduard Fuchs, CSc. (lecturer)
Guaranteed by
doc. RNDr. Eduard Fuchs, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Fri 10:00–11:50 M5,01013
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
there are 7 fields of study the course is directly associated with, display
Course objectives
Some formal aspects of mathematics are studied. The main objectives of the couurses is the Godel theorem of incompleteness.
Learning outcomes
After completion of the course the student will get an idea about the formal construction of mathematical theories and about Godel's theorem of incompleteness.
Syllabus
  • Origins of set theory and its impact on the 20th century mathematics.
  • Formalization of mathematics: propositional calculus, first order logic calculus, axiomatic theories.
  • Axioms for set theory: Zermelo-Fraenkel set theory and Gödel-Bernays set theory, construction of natural and real numbers in set theory.
  • Cardinal and ordinal numbers: ordering and arithmetics of cardinal numbers, arithmetics of ordered sets, ordinal types and their arithmetics, well-ordering sets, ordinal numbers, transfinite induction.
  • Axiom of choise and equivalent theorems.
  • Peano arithmetics.
Literature
    recommended literature
  • FUCHS, Eduard. Teorie množin pro učitele. 1st ed. Brno: Masarykova univerzita, 1999. info
  • Set theory and its applications : annual boise extravaganza in set theory, Boise, Idaho, 1995-2010. Edited by L. Babinkostova. Providence, R.I.: American Mathematical Society, 2011, xi, 330. ISBN 9780821848128. info
  • Handbook of set theory. Edited by M. Foreman - Akihiro Kanamori. Dordrecht: Springer, 2010, xiv, s. ISBN 9781402048432. info
  • TARSKI, Alfred. A Formalization of set theory without variables. Providence: American Mathematical Society, 1987, xxi, 318. ISBN 0821810413. info
Teaching methods
Theoretical explanation with practical examples
Assessment methods
Written test (50 % success rate)
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2025/MUC61