Title of the course: Introduction to Forcing
Instructor: Assoc. Prof. Ahmet Çevik
Institution: JSGA/ODTÜ
Dates: 9-14 August 2021
Prerequisites: Set theory, basic understanding of models and satisfaction.
Level: Graduate
Abstract: This is a graduate level course on forcing. Forcing method was introduced by Paul Cohen in his independency proof of the Continuum Hypothesis (CH). It shortly became a powerful method and it has been used in many applications of set theory and recursion theory. In our lecture, we will have a gentle introduction to forcing and will prove the consistency of the negation of CH. For this we will cover models of set theory, relativization, reflection principle, forcing notions, generic sets, P-names, language of forcing, fundamental theorems of forcing, and consistency proof of the negation of CH. Due to the fact that this will be a one week module, unfortunately there will not be enough time to review set theory. Thus, a solid background on set theory (particularly ordinals, cardinals, and transfinite induction) is required, as well as some intuitive understanding of the concept of structures and models.
Language: TR, EN