Appalachian set theory

Saturday, November 5, 2016

9:30 a.m. - 6 p.m. with coffee and lunch breaks

Carnegie Mellon University

Lectures in Doherty 2302

Refreshments in Wean Hall 6220

Breakfast and coffee starting at 8:30

Maryanthe Malliaris : "Cofinality spectrum problems: 𝔭, 𝔱 and model theory"

Description

The workshop will motivate and go through the main proofs of the recent Malliaris-Shelah paper "Cofinality spectrum theorems in model theory, set theory and general topology."

Although this is a technical paper, at its core is a series of natural ideas and images, and the aim of the workshop will be to explain this core as directly as possible.

We will see why the two problems solved by the paper, that 𝔭=𝔱 and that SOP₂ is maximal in Keisler's order, can be seen as instances of a more fundamental problem involving a comparison of orders and trees, and we will go through the main steps in the analysis of these so-called cofinality spectrum problems. Along the way we will discuss the larger picture of Keisler's order along with some model-theoretic classification theory.

Suggested reading

• The main reference: Malliaris and Shelah, "Cofinality spectrum theorems in model theory, set theory, and general topology." Journal of the American Mathematical Society 29 (2016), 237-297 (arxiv, journal).
• Basics of ultrafilters and ultrapowers, including definitions of regular ultrafilters and good ultrafilters: Chang and Keisler, Model Theory, third edition, sections 4.1 (the fundamental theorem), 4.3 (regular ultrapowers), and 6.1 (ultraproducts which are saturated).
• Original reference for Keisler's order: H. J. Keisler, "Ultraproducts which are not saturated." Journal of Symbolic Logic 32 (1967) 23-46.

Local information

The nearest airport is Pittsburgh International Airport. The Supershuttle shared van service is cheaper but slower than taking a taxi from the airport.

Lodging

VERY IMPORTANT NOTE ABOUT LODGING: A block of rooms earmarked for attendees has been set aside at a local hotel (the Shadyside Inn). If we are covering your lodging expenses then we will need to make a reservation for you. Please don't make your own reservation if we have promised you support, this will cause confusion and may make it impossible for us to reimburse you.

Participant travel support

Funds provided by the National Science Foundation will be used to reimburse some participant transportation and lodging expenses. Priority will be given to students and faculty who do not hold federal research grants. Please request such funds as far in advance of the meeting as possible by sending the following information to the email address appalachiansettheory@gmail.com

• Your name, university affiliation, mailing address, phone number and email address
• Your nationality and visa status
• Your professional status and some additional information:
  • Undergraduate students: please describe your background in set theory
  • Graduate students: please tell us your year and the name of your thesis advisor if you have one
  • Faculty: please tell us whether you hold a federal research grant
• A brief statement about your interest in the workshop