Title: The model theory of countable abelian p-groups
Speaker: Ivo Herzog (OSU)
Abstract: The countable abelian p-groups that have no divisible summands are determined, up to isomorphism, by their Ulm invariants. This classification can be used to determine the homogeneous countable abelian p-groups. One such abelian p-group turns out to be a universal countable abelian p-group for purity, i.e., every countable abelian p-group admits a pure embedding into it. It is the last step needed to complete the solution to Fuchs' Problem 5.1 below $\aleph_{\omega}$.
We will start off with some background, including how Ulm's Theorem is used to obtain a Scott sentence as well as some motivating examples. This is joint work with Marcos Mazari Armida.
URL associated with Seminar: https://research.math.osu.edu/logicseminar/