Abstract: 

This talk will be about the limit theory of numerical semigroups, namely, cofinal submonoids of the natural numbers. The basic example is the following: Let $a$ and $b$ be relatively prime natural numbers, and consider all linear combinations of $a$ and $b$ with non-negative integer coefficients. It is an elementary (and well known) fact to show that these are all cofinite. These are precisely the numerical semigroups with two generators.

The talk will concentrate on the theory of ultraproducts of numerical semigroups with two generators. We will explain why we believe that this theory is definable, and exhibit a complete axiomatization in some particular cases.

Venue: Quan 9

Zoom Room: 717 463 6082