PLS 2026 Short Summer School (Pre-Symposium)

This edition of PLS will host a short summer school during July 2–4, 2026, aimed primarily at students. Participation is open to advanced undergraduates, MSc and PhD students, postdoctoral researchers, and anyone interested in logic. The goal of the summer school is to prepare participants for this year’s main tutorials by Maryanthe Malliaris and Alexander S. Kechris.

In order to attend please register here: https://forms.gle/rYahrNHjQGeunFBBA

The Short Summer School will feature the following crash courses:

Model Theory

Instructor: Adele Padgett (University of Vienna)
Title: The unstable formula theorem in model theory

Abstract

An important theme in model theory is to study the mathematical structures satisfying a collection of axioms with some interesting property. Stability is one of the most important of these properties. Stable theories are very natural from a model theoretic perspective and have also helped solve problems in other areas of mathematics, including graph theory, additive combinatorics, differential algebra, and Diophantine geometry. This tutorial will focus on Shelah’s Unstable Formula Theorem. Along the way, we will develop key notions in basic model theory and learn various ways of thinking about stability.

Descriptive Set Theory

Instructor: Forte Shinko (UC Berkeley)
Title: Introduction to descriptive set theory and classification problems

Abstract

One of the trademark applications of logic to the rest of mathematics is to formalize and prove impossibility results, and more broadly, to compare the difficulty of various naturally-occurring problems. For instance, the informal assertion that “it is hard to tell whether a finite graph has a 3-coloring” can be made precise via the statement that deciding 3-colorability is NP-complete; more generally, in the context of finite objects, one typically works in the language of complexity theory and computability theory. Analogously, descriptive set theory provides a framework to formalize problems concerned with objects specified by a countable amount of data (e.g. real numbers, manifolds, finitely generated groups). We will give an introduction to descriptive set theory, with a view towards the modern program of comparing classification problems via the formalism of Borel reducibility of equivalence relations.

Set Theory

Instructor: Benjamin Siskind (TU Wien)
Title: Determinacy and large cardinals

Abstract

Many natural questions about simply definable sets of reals are independent of the usual axioms of set theory. However, if we add large cardinal axioms, which assert the existence of large infinite sets beyond what can be shown to exist from the usual axioms alone, we can decide many of these natural questions. This is because the existence of large cardinals implies determinacy principles that state certain infinite two player games are determined; that is, one of the players has a winning strategy. In this tutorial, we will show how determinacy principles can be used to answer some natural questions about definable sets of reals and also prove certain determinacy principles, both from the usual axioms but also from large cardinal axioms.