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Course, academic year 2023/2024
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Introduction to Set Theory 2 - NMAG439
Title: Úvod do teorie množin 2
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2023 to 2023
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: English, Czech
Teaching methods: full-time
Teaching methods: full-time
Guarantor: RNDr. David Chodounský, Ph.D.
doc. Mgr. Radek Honzík, Ph.D.
Class: M Mgr. MSTR
M Mgr. MSTR > Povinně volitelné
Classification: Mathematics > Algebra
Annotation -
This is a follow up cours for the basic set theory course. Students will learn basic concepts of infinitary combinatorics and set theoretic topics beyond the fundamentals.
Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (21.05.2021)
Course completion requirements -

Credit will be awarded for active participation.

Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (21.05.2021)
Literature -

B. Balcar, P. Štěpánek, Teorie množin, Academia, Praha 2001.

Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (21.05.2021)
Syllabus -

Topics:

constructible sets,

independent partitions,

Hewit-Marczewski-Pondiczery theorem, almost disjoint systems,

Δ-system lemma,

theorem on free sets,

stationary sets and Fodor's lemma,

Ulam matrix,

Silver's theorem,

combinatorial principles diamond and square,

uncountable linear orders,

Suslin line and Suslin tree, Kurepa tree,

Aronszajn trees, Ramsey theorem and its canonical version,

partition relations,

Galvin-Prikry theorem,

Erdös-Dushnik-Miller theorem,

Erdös-Rado theorem.

Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (21.05.2021)
 
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