SUBJECT

Title

Set theory I

Type of instruction

lecture

Level

master

Part of degree program
Credits

6

Recommended in

Semesters 1-4

Typically offered in

Autumn/Spring semester

Course description

Cofinality, Haussdorff’s theorem. Regular, singular cardinals. Stationary sets. Fodor’s theorem. Ulam matrix. Partition relations.  Theorems of  Dushnik-Erdős-Miller, Erdős-Rado. Delta systems. Set mappings. Theorems of  Fodor and Hajnal. Todorcevic’s theorem. Borel, analytic, coanalytic, projective sets. Regularity properties. Theorems on separation, reduction. The hierarchy theorem. Mostowski collapse. Notions of forcing. Names. Dense sets. Generic filter. The generic model. Forcing. Cohen’s result.

Readings

A. Hajnal, P. Hamburger: Set Theory. Cambridge University Press, 1999.