Notes on Cofinality Spectrum Problems

TL;DR

This paper discusses cofinality spectrum problems in model theory, set theory, and topology, highlighting key arguments and proofs related to cardinal invariants and classification of theories.

Contribution

It provides a detailed exposition of the setup and main arguments from Malliaris and Shelah's work on cofinality spectrum problems, including the proof that rak{p} = rak{t} and the maximality of SOP_2 theories.

Findings

Proof that rak{p} = rak{t}

SOP_2 theories are maximal in Keisler's Order

Clarification of key arguments in cofinality spectrum problems

Abstract

These notes are based on Appalachian Set Theory lectures given by M. Malliaris on November 5, 2016 with D. Casey as the official scribe. The aim of the lectures was to present the setup and some key arguments of "Cofinality spectrum problems in model theory, set theory and general topology" by Malliaris and Shelah. This provides a sketch of the proof that $\mathfrak{p} = \mathfrak{t}$ and that $SOP_2$ theories are maximal in Keisler's Order.