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Course, academic year 2022/2023
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Set Theory - NAIL063
Title: Teorie množin
Guaranteed by: Department of Applied Mathematics (32-KAM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2019
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
Virtual mobility / capacity: no
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Teaching methods: full-time
Additional information:
Guarantor: doc. Mgr. Jan Kynčl, Ph.D.
doc. Mgr. Robert Šámal, Ph.D.
Class: Informatika Bc.
Classification: Informatics > Theoretical Computer Science
Incompatibility : NLTM030, NMIN160
Interchangeability : NMIN160
Is co-requisite for: NAIL124
Is incompatible with: NLTM030, NAIL003
Is interchangeable with: NAIL003
Annotation -
Last update: G_I (28.05.2004)
An introductory course to set theory.
Aim of the course - Czech
Last update: T_KTI (26.05.2008)

Naučit základy teorie množin

Course completion requirements -
Last update: doc. Mgr. Jan Kynčl, Ph.D. (31.05.2019)

Written exam.

Literature - Czech
Last update: doc. Mgr. Robert Šámal, Ph.D. (02.03.2017)
  • B. Balcar, P. Štěpánek, Teorie množin, Academia, Praha 1986
  • K. Kunen, Set Theory, North Holland 1980
  • B. Balcar, P. Štěpánek, Teorie množin, skriptum MFF UK, Praha 1974, 1980
  • Paul R. Halmos: Naive Set Theory, Springer 1998/Martino Fine Books 2011 (reprint, orig. ed. 1960)
  • Karel Hrbacek, Thomas Jech: Introduction to Set Theory, 3.ed., Marcel Dekker, 1999
  • Raymond M. Smullyan: Set Theory and the Continuum Problem, Dover Books on Mathematics, 2010

Requirements to the exam -
Last update: doc. Mgr. Jan Kynčl, Ph.D. (14.02.2019)

For the English class, the exam will be written based on the material that was presented.

Syllabus -
Last update: doc. Mgr. Jan Kynčl, Ph.D. (13.02.2020)

1. Historical background, axioms of ZFC.

2. Basic operations: inclusion, intersection, difference, pairs, cartesian product, relation, function.

3. Ordering, well-ordering, ordinal numbers, natural numbers, basics from ordinal arithmetic.

4. Countable and uncountable sets, cardinal numbers, Cantor-Bernstein theorem, cardinal arithmetics.

5. Classes and relations, transfinite induction and recursion.

6. Axiom of choice and its equivalents.

7. Elements of infinitary combinatorics: Konig's lemma, Compactness principle, Ramsey theorem.

For details see

In 2019/2020, there is an optional exercise for this course (Exercises from set theory - NAIL124).

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