To develop notions and techniques which can be used both inside set theory and in other areas of contemporary mathematics.
Mostowski collapse and elementary relative consistency proofs;
the reflection theorem;
constructible sets and consistency of AC and GCH;
forcong and consistency of not CH, CH + not GCH, and diamond.
K. Kunen, Set Theory. An Introduction to Independence Proofs, North-Holland, 1980
K. Kunen, Set Theory, College Publications, 2011 (the “new” edition of the previous text)
K. Cieselski, Set Theory for the Working Mathematician, Cambridge UP, 1997
T. Jech, Set theory. The third millenium edition, Springer, 2003