`2022-10-04 13:50:00``2022-10-04 14:45:00``The model theory of countable abelian p-groups``Title: The model theory of countable abelian p-groupsSpeaker: 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/``Enarson 206``OSU ASC Drupal 8``ascwebservices@osu.edu``America/New_York``public`

`2022-10-04 13:50:00``2022-10-04 14:45:00``The model theory of countable abelian p-groups``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/``Enarson 206``Department of Mathematics``math@osu.edu``America/New_York``public`**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/