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Introduction to forcing, spring 2014

 

DATES: FEBRUARY 3-6 AND 10-13

Lecturer

Daisuke Ikegami

Scope

 sp.

Type

Advanced studies

Prerequisites   

During the course, we assume the familiarity of the basics of ordinals & cardinals, and of the transfinite induction & recursion. We also mention some basic facts about the Gödel's constructible universe.

Contents

In this course, we cover the basic theory of forcing, a basic method of constructing a model of set theory, and we use it to prove the consistency of ZFC + "the negation of the Continuum Hypothesis" assuming the consistency of ZFC. If time permits, we also show the consistency of ZF + "the negation of the Axiom of Choice" assuming the consistency of ZFC and cover some applications of forcing.

Lectures

Monday February 3 and 10 from 14-16 in room BK106
Tuesday February 4 and 11 from 14-16 in room C130
Wednesday February 5 and 12 from 14-16 in room CK108
Thursday February 6 and 13 from 14-16 in room BK106

Exams

 

Bibliography

 

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