Fudan Logic Seminar 2025

July 30

Location: HGX208

Speaker: Alf Onshuus

Time: 9:30 - 10:30

On the limit theory of numerical semigroups with two generators

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.

July 23

Location: HGX208

Speaker: Joel David Hamkins

Time: 14:30 - 15:30

Computable surreal numbers

I shall give an account of the theory of computable surreal numbers, proving that these form a real-closed field. Which real numbers arise as computable surreal numbers? You may be surprised to learn that some noncomputable real numbers are computable as surreal numbers, and indeed the computable surreal real numbers are exactly the hyperarithmetic reals. More generally, the computable surreal numbers are exactly those with a hyperarithmetic surreal sign sequence. This is joint work with Dan Turetsky, but we subsequently found that it is a rediscovery of earlier work of Jacob Lurie.