[theory students] logic courses

[Dieter van Melkebeek <dieter@xxxxxxxxxxx>]

Dear all,

The faculty of the logic group in the math department asked to announce 
the following courses, which they will offer in Spring 2019.

 Â-- Dieter

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Math 773: Computability Theory (J. Miller).
Time / Location: TuTh 11:00AM - 12:15PM, Van Vleck B321

This is an introductory course in Computability (nÃe Recursion) theory. 
Computability theory is a branch of mathematical logic that goes back to 
work of Turing, Church, and Kleene on formalizing the concept of an 
algorithm. The core notion in computability theory is that of a 
computable set of natural numbers, a set whose members can be determined 
by an algorithm. There are incomputable sets of natural numbers that 
occur naturally in mathematics, e.g., the set of (codes of) integer 
polynomials in several variables that have integer roots. Incomputable 
sets of natural numbers can be compared with respect to their 
algorithmic complexity. A set A is Turing reducible to a set B if there 
is an algorithm to determine membership in A using B as data. By 
identifying sets that are reducible to each other we obtain a partial 
order, the Turing degrees. In this course, we will introduce this model 
of relative computation along with contemporary methods for analyzing 
this structure that range from purely combinatorial techniques to more 
sophisticated tools, such as the forcing method and the priority method. 
(No previous knowledge of logic is required.)

A list of topics can be found here: 
https://www.math.wisc.edu/773-Computability-Theory

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Math 776: Model Theory (O. Mermelstein)
Time / Location: TuTh 9:30AM - 10:45AM, Van Vleck B235

Model Theory investigates properties and unifying themes of first order 
structures and theories. Why is this good if I do not wish to research 
first order structures, you ask? Good question.
In short, acquaintance with Model Theory is another tool in one's 
toolbox, another layer of abstraction. Much like the study of groups has 
a different flavor to the study of a specific group, zooming further out 
to the bare-bones first order properties of groups has its merits. Model 
Theory offers a unifying, bird's eye view of some phenomena occurring in 
distinct regions of mathematics, and the means to formalize of how these 
regions differ.

In this introductory course we will cover the basic definitions, methods 
and results needed to internalize this additional perspective.

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Math 873: Advanced Topics in Foundations (S. Lempp)
Time / Location: MoWeFr 2:25PM - 3:15PM, Van Vleck B321

Topic: Computability-theoretic and proof-theoretic aspects of partial 
and linear orderings

I plan to cover a lot of material from the past 35 years on computable
partial and linear orderings. This is an area where they are still
quite a few open problems appropriate for thesis work! I also plan to
touch on some reverse math implications of these results. Given time, I 
may touch on Boolean algebras toward the end.

The prerequisite is Math 773 (taken concurrently is fine).