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Course, academic year 2023/2024
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Forcing - NLTM003
Title: Forsing
Guaranteed by: Department of Theoretical Computer Science and Mathematical Logic (32-KTIML)
Faculty: Faculty of Mathematics and Physics
Actual: from 2016
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: cancelled
Language: English
Teaching methods: full-time
Teaching methods: full-time
Class: DS, algebra, teorie čísel a matematická logika
Mat. logika a teorie množin
Classification: Informatics > Theoretical Computer Science
Incompatibility : NMAG575
Interchangeability : NMAG575
Is incompatible with: NMAG575
Is interchangeable with: NMAG575
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: G_I (05.11.2001)
Aim of the course - Czech

Naučit teorii kardinálních čísel a metodu forsingu

Last update: T_KTI (26.05.2008)
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_KTI (19.05.2005)
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_KTI (19.05.2005)
 
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