Duarte Maia - An Introduction to Reverse Math

Recorded as part of the CFvW Colloquium on July 10, 2024 An Introduction to Reverse Math - Duarte Maia (University of Chicago) Talk abstract: Reverse Math is a relatively recent (mid 70's) branch of logic, which can in some sense be seen as formalizing the question: "What does it mean for a theorem to imply another?" This is slightly more difficult than it may seem. Clearly we cannot be referring to logical implication: Otherwise, since every theorem is true by definition, by the truth table for implication any two theorems imply each other... A possible way to interpret it (aside from the colloquial "I know it when I see it") is to consider implication within a weaker set of axioms, weak enough that the theorems that you care about aren't necessarily true to begin with, and so implications between them are nontrivial. In this talk, I'll introduce you to the most common base system, called RCA0 (R-C-A-Nought), and I'll walk you through some of the basics of reverse math, explaining how some theorems which may at first seem completely unrelated are actually equivalent. Explore our colloquium schedule on our website: https://uni-tuebingen.de/en/research/centers-and-institutes/carl-friedrich-von-weizsaecker-center/news-and-events/carl-friedrich-von-weizsaecker-colloquium/