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Course, academic year 2019/2020
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Forcing - NMAG575
Title in English: Forsing
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2019
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Guarantor: RNDr. David Chodounský, Ph.D.
Class: DS, algebra, teorie čísel a matematická logika
Mat. logika a teorie množin
M Mgr. MSTR
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
Annotation -
Last update: T_KA (28.04.2016)
Forsing is a method for constructions of models of set theory. It is a method for verifying unprovability or consistency of various mathematical statements.
Aim of the course - Czech
Last update: T_KA (28.04.2016)

Naučit teorii kardinálních čísel a metodu forsingu

Course completion requirements - Czech
Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (11.06.2019)

Předmět je zakončen ústní zkouškou.

Literature - Czech
Last update: T_KA (28.04.2016)
  • 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

Requirements to the exam - Czech
Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (13.10.2017)

Zkouška je pouze ústní, požadavky ke zkoušce odpovídají sylabu předmětu v rozsahu prezentovaném na přednášce.

Po domluvě může být zkouška udělena i na základě kompetentní prezentace referátu na zadané téma na některém ze seminářů (seminář z forcingu, seminář z počtů).

Syllabus -
Last update: T_KA (28.04.2016)

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

 
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