Aditi Sundaram, Three Consistencies, Three Theories: An Exploration of Standard, Tableau, and Slow Consistency in each of Σ12, EA, and Supexp, April 16, 2019
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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 S12, EA, and Supexp Abstract. When we deal with systems of arithmetic of sufficient strength (namely, systems that can interpret I0 + 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 I0 + 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 (Σ12, 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 Σ12, is an Orey sentence for Σ12, and the Slow consistency statement for Σ12, is an Orey sentence for EA. This talk uses concepts predominantly from first-order logic and proof theory, but also touches upon a few areas of modal logic, set theory, and computational complexity. |