1st Semester 2014/15: Introduction to Forcing

Instructors

Hugo Nobrega
If you are interested in this project, please contact the instructor by email.

ECTS

6

Description

Forcing is a fundamental model-construction tool in set theory, originally introduced by Paul Cohen in the 1960s in order to establish the independence of the axiom of choice and the continuum hypothesis from the axioms of ZF.

In this project, we will learn the basics of this technique by reading the relevant chapter in (one of the editions of) the classical reference text:

• Kenneth Kunen, Set Theory: an introduction to independence proofs. Elsevier, 1980.
• Kenneth Kunen, Set Theory. College Publications, 2011.

Our concrete goal will be to understand the proof of the independence of the continuum hypothesis from ZFC.

Organisation

This will be a "classical" reading group: we will meet twice a week in the last 3 weeks of January, and during each meeting a piece of the reference text will be determined, which the students are to read by the following meeting, when it will be discussed.

Prerequisites

A basic set theory course (up to cardinal arithmetic) and general mathematical maturity.

Assessment

Students will be assessed on a pass/fail basis, with an oral exam at the end of the project. Active participation in the group discussions will contribute to the assessment.