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)
Metoda na konstrukce modelů teorie množin a prokazování nedokazatelnosti
nebo bezespornosti různých matematických tvrzení.
Aim of the course - Czech
Last update: T_KA (28.04.2016)
Naučit teorii kardinálních čísel a metodu forsingu
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
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
Last update: T_KA (28.04.2016)
1. Axiomatika teorie množin: Zermelova a Frankelova, axiomy Gödela a Bernayse.
2. Pojem nezávislosti formule, konzistence a ekvikonzistence teorií.
3. Modely teorie množin, modelová třída, rozšíření tranzitivného modelu, absolutnost formulí.