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Logic Seminar

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Department of Mathematics, The Ohio State University

Hello! Welcome to the website for the Logic Seminar in the Ohio State Department of Mathematics. We normally meet on **Tuesdays** from **1:50–2:45pm** in **Enarson 206**. To join on Zoom or to be added to our mailing list, please contact Nigel Pynn-Coates at pynn-coates.1@osu.edu.

### Upcoming Seminars (2022–2023)

#### October 4

Ivo Herzog (OSU)

**Title:** The model theory of countable abelian p-groups

**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 ℵ_{ω}.

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.

#### October 11

Alexi Block Gorman (McMaster)

**Title:** TBA

**Abstract:** TBA

Elliot Kaplan (McMaster)

**Title:** TBA

**Abstract:** TBA
#### October 18

Liling Ko (OSU)

**Title:** TBA

**Abstract:** TBA
### Past Seminars (2022–2023)

#### September 20

Nigel Pynn-Coates (OSU)

**Title:** Monotone T-convex T-differential fields

**Abstract:** Let T be a suitably nice o-minimal theory extending the theory of real closed fields. A T-convex T-differential field is an expansion of a model of T by a valuation and a derivation, each of which is compatible with the o-minimal structure, the former in the T-convex sense of van den Dries–Lewenberg and the latter in the sense of Fornasiero–Kaplan. When T is the theory of the real field with restricted analytic functions, we can expand an ordered differential Hahn field (a kind of generalized power series field) to a T-convex T-differential field, in which case the derivation is monotone, i.e., weakly contractive with respect to the valuation (monotone differential Hahn fields were studied earlier by Scanlon and Hakobyan). I will describe joint ongoing work with Kaplan on monotone T-convex T-differential fields, achieving among other results an Ax–Kochen/Ershov type theorem for such structures. A key step is isolating an appropriate analogue of henselianity in this setting. I will explain these terms.
#### September 6

Kyle Gannon (UCLA)

**Title:** Extension domination

**Abstract:** Motivated by the theory of domination for types, we introduce a notion of domination for Keisler measures called extension domination. We argue that this variant of domination behaves similarly to its type setting counterpart. We prove that extension domination extends domination for types and that it forms a preorder on the space of global Keisler measures. We then explore some basic properties related to this notion. This is joint work with Jinhe Ye.
#### August 30

Matthew DeVilbiss (OSU)

**Title:** Towards a general method for showing strong minimality of differential equations

**Abstract:** In this talk, I will outline a technique for showing that nonlinear algebraic differential equations are strongly minimal. This is used to prove the strong minimality of generic differential equations with sufficiently large degree, answering a question of Poizat (1980). I will also discuss ongoing work in applying this method to differential equations of interest whose coefficients are not generic. This is joint work with James Freitag.

This page is currently maintained by Nigel Pynn-Coates.