MUC62 Set Theory

Faculty of Science
Spring 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
Prerequisites (in Czech)
MUC61 Foundations of mathematics || M7532 Foundations of mathematics
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
First course of set theory. Cardinal and ordinal numbers, transfinite induction.
Learning outcomes
At the end of the course the student is oriented in the following terms: Cardinal and ordinal numbers, transfinite induction.
Syllabus
  • Problems of infinity in mathematics. Origins of set theory and its impact on the 20th century mathematics. 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 choice and equivalent theorems.
Literature
    recommended literature
  • FUCHS, Eduard. Teorie množin pro učitele. 1st ed. Brno: Masarykova univerzita, 1999. info
    not specified
  • FUCHS, Eduard. Základy teorie množin. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1986, 146 s. info
  • FUCHS, Eduard. Logika a teorie množin : (úvod do oboru). Vyd. 1. Brno: Rektorát UJEP, 1978, 175 s. info
  • TARSKI, Alfred. Úvod do logiky a metodologie deduktivních věd. Translated by Pavel Materna. Vyd. 1. Praha: Academia, 1966, 245 s. URL info
Teaching methods
Theoretical explanation online
Assessment methods
Test, oral exam.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024.
  • Enrolment Statistics (recent)
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