The model theory of countable abelian p-groups

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Logic Seminar
October 4, 2022
1:50PM - 2:45PM
Location
Enarson 206

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Add to Calendar 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
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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/

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