Forcing - NMAG575
Title: Forsing
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: Czech, English
Teaching methods: full-time
Teaching methods: full-time
Additional information:
Guarantor: RNDr. David Chodounský, Ph.D.
Class: DS, algebra, teorie čísel a matematická logika
Mat. logika a teorie množin
M Mgr. MSTR > Povinně volitelné
M Mgr. MSTR > Volitelné
Classification: Mathematics > Mathematics, Algebra, Differential Equations, Potential Theory, Didactics of Mathematics, Discrete Mathematics, Math. Econ. and Econometrics, External Subjects, Financial and Insurance Math., Functional Analysis, Geometry, General Subjects, , Real and Complex Analysis, Mathematics General, Mathematical Modeling in Physics, Numerical Analysis, Optimization, Probability and Statistics, Topology and Category
Incompatibility : NLTM003
Interchangeability : NLTM003
Is incompatible with: NLTM003
Is interchangeable with: NLTM003
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Annotation -
Forsing is a method for constructions of models of set theory. It is a method for verifying unprovability or consistency of various mathematical statements.
Last update: T_KA (28.04.2016)
Aim of the course - Czech

Naučit teorii kardinálních čísel a metodu forsingu

Last update: T_KA (28.04.2016)
Course completion requirements -

Students have to pass final oral exam.

Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (28.10.2019)
Literature - Czech
  • B. Balcar, P. Štěpánek: Teorie množin, Academia Praha, 1986
  • K. Kunen: Set Theory, An Introduction to Independence Proof, North Holland P. C., 1980
  • D. H. Fremlin: Consequences of Martin's Axiom, Cambridge University Press, 1984
  • T. Jech: Set Theory, Academic Press, 1978
  • S. Shelah: Proper Forcing, Lecture Notes in Math. 940, 1982
  • A. Kanamori: The Higher Infinite, Springer-Verlag, 1994

Last update: T_KA (28.04.2016)
Requirements to the exam -

Students have to pass final oral exam. The requirements for the exam correspond to what has been done during lectures.

Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (28.10.2019)
Syllabus -

Axiomatization of set theory: Zermelo-Frankel, axioms of Gödel and Bernays

Independent formulas, consistency and equiconsistecy of theories

Models of set theory, model class, extension of transitive model, absolute formulas

Ultrapower, measurable cardinal number, elementary injection, supercompact cardinal number

Generic filter, generic extension of transitive model, boolean names, forcing

Martin axiom, PFA (Proper forcing axiom), Martin's maximum

Examples of forcing: addition of real number, continuum can be arbitrary huge, collapsing of cardinal numbers, Levy's collaps

Suslin hypothesis

Iteration, consistency of Martin axiom

Last update: T_KA (28.04.2016)