# Course Descriptions

## 16:640:569 - Selected Topics in Logic

Please note: the instructor and course information changes from semester to semester for this course number.  Specifics for each semester below.

## Spring 2018

Grigor Sargsyan

Subtitle:  Introduction to Logic

## Course Description:

This is a basic logic course covering topics from recursion theory, model theory and set theory. The following is the list of topics that we will cover.

1. compactness theorem and incompleteness theorem (0-1 laws and etc).

2. Back and fourth arguments (uniqueness of countable dense orders)

3. quantifier elimination and applications to algebra (Hilberts Nullstelenzats and etc)

4. Godel's constructible universe (Consistency of Axiom of Choice and Continuum Hypothesis relative to ZF)

5. Cohen's forcing (Consistency of negation of CH relative to ZFC)

Students interested in doing research in logic who have not yet passed their qualifying exam must take this course. Students interested in other areas of mathematics will profit from this course as well, as basic methods developed by logicians have found applications in many areas of mathematics, and this course will be an introduction to some of these methods.

## Text:

A Concise Introduction to Mathematical Logic, Rautenberg

## Prerequisites:

General Mathematical Maturity

## Fall 2017

Simon Thomas

Subtitle: Countable Borel Equivalence Relations

### Course Description:

This course will be an introduction to countable Borel equivalence relations, a very active area of classical descriptive set theory which interacts nontrivially with such diverse areas of mathematics as model theory, computability theory, group theory and ergodic theory. The topics to be covered will include applications of superrigidity theory to countable Borel equivalence relations, as well as some recent applications of Borel determinacy. No prior knowledge of superrigidity or determinacy will be assumed.

None

## Prerequisites:

Familiarity with the basic theory of complete separable metric spaces and their Borel subsets

### Schedule of Sections:

For more information on instructors and sections for Fall 2017, please see our Fall 2017 Teaching Schedule Page

For more information on instructors and sections for this course for other semesters, please see our Teaching Schedule Page

## Contacts

Departmental Chair
Michael Saks