SubjectsSubjects(version: 845)
Course, academic year 2018/2019
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Set Theory - NLTM001
Title in English: Teorie množin
Guaranteed by: Department of Theoretical Computer Science and Mathematical Logic (32-KTIML)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018 to 2018
Semester: summer
E-Credits: 6
Hours per week, examination: summer s.:2/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: not taught
Language: Czech, English
Teaching methods: full-time
Guarantor: doc. RNDr. Josef Mlček, CSc.
Class: DS, algebra, teorie čísel a matematická logika
Mat. logika a teorie množin
Classification: Informatics > Theoretical Computer Science
Annotation -
Last update: T_KTI (11.04.2001)
Ordinal and cardinal numbers, well-founded relations, isomorphism theorem, reflection principle. Transitive models, constructible sets, ultrapowers, measurable cardinals, Scott's theorem. Forcing and Boolean-value models, a consistency of negation of the continuum hypothesis. Nonstandard set theory, axiom of superuniversality, elementary embedding of the universe into a transitive class, standard, internal and external sets.
Aim of the course - Czech
Last update: RNDr. Jan Hric (07.06.2019)

Naučit zákaldy teorie množin

Literature - Czech
Last update: RNDr. Pavel Zakouřil, Ph.D. (05.08.2002)
  • B. Balcar, P. Štepánek: Teorie množin, Academia, Praha 1986
  • K.D. Stroyan, W.A.J. Luxemburg: Introduction to the theory of infinitesimals, Academic Press, New York, 1967

Syllabus -
Last update: T_KTI (19.05.2004)

Ordinal and cardinal arithmetic. The axiom of regularity. The cummulative hierarchy of sets.

Well-founded relations and induction. Collapsing theorems. Transitive models. Constructible sets.

Consistence of the axiom of choice and the generalization continuum hypothesis.

Ultrapowers and elementary embeddings. Measurable and inaccessible cardinals.

Bulean-valued models, generic extensions. Independence of the continuum hypothesis.

Non-regular set theory with strong choice and with the axiom of superuniversality. Nonstandard methods.

Applications.

 
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