
Aditi will give the math table talk next Tuesday (April 16nd). His
title and abstract are below.
Speaker: Aditi Sundaram, April 16, 2019
Title. Three Consistencies, Three Theories: An Exploration of Standard,
Tableau, and Slow Consistency in each of S^{1}_{2}, EA, and Supexp
Abstract. When we deal with systems of arithmetic of sufficient strength (namely, systems that
can interpret I_{0} + SUPEXP, various things that one might mean by "system S is consistent"
come out as equivalent; but when we zoom in and look at systems that are weaker in terms of
interpretability than I_{0} + SUPEXP, these various statements come apart in an interesting way.
We will explore several case studies of this phenomenon by defining and examining three
different senses of consistency (Standard, Tableau, and Slow) in three systems of arithmetic
(Σ^{1}_{2}, EA, and Supexp). Our main results will show that while the Standard consistency
statement is not an Orey sentence for any theory, the Tableau consistency statement for
Σ^{1}_{2}, is an Orey sentence for Σ^{1}_{2}, and the Slow consistency statement for
Σ^{1}_{2}, is an Orey sentence for EA.
This talk uses concepts predominantly from firstorder logic and proof theory, but also touches upon a few areas of modal logic, set theory, and computational complexity.
