Advanced Set Theory

Quick Info. Reading course.

Description. This course examines the central role of forcing in contemporary set theory, highlighting its power to establish independence results beyond the reach of ZFC. It focuses on classical outcomes such as Cohen’s proof of the independence of the Continuum Hypothesis, situating forcing methods within the broader development of modern set theory.

Syllabus. The course has two possible tracks, depending on the taste of the student. Track Classic: Forcing methods and independence results. Track Algebraic: Boolean valued models of Set theory, Forcing methods and independence results.

Bibliography.

• Set Theory by Kunen, Chapters 7 and 8 (and 5 and 6 if time allows).

  Reference book for Track A.

• The forcing method in Set Theory by Viale Chapters 6 and 7.

  Reference book for Track B.