Isabella Scott : The reverse mathematics of existence of ideals in commutative rings

Posted by William Adkisson , part of the Louise Hay Logic Seminar.

At

Nov. 28, 2022, 5 p.m.

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Abstract

Abstract: Revisiting Kronecker's claim that "God created the integers, all else is the work of man", let's take a look at just how much of mathematics can be formalised in arithmetic. Since a lot of mathematics requires forming sets, we'll allow ourselves some set existence axioms, but we'll be suspicious of them, because, well, we're not sure if they have divine approval. In the interest of time, we won't talk about all of mathematics, but we'll focus on a couple of theorems about the existence of ideals in commutative rings.