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THE EMBEDDING PROPERTY FOR SORTED PROFINITE GROUPS

Part of: Other classes of algebra Model theory

Published online by Cambridge University Press:  20 March 2023

JUNGUK LEE Open the ORCID record for JUNGUK LEE [Opens in a new window]
JUNGUK LEE*
Affiliation:
DEPARTMENT OF MATHEMATICS CHANGWON NATIONAL UNIVERSITY CHANGWON 51140 SOUTH KOREA
*
E-mail: ljwhayo@changwon.ac.kr
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Abstract

We study the embedding property in the category of sorted profinite groups. We introduce a notion of the sorted embedding property (SEP), analogous to the embedding property for profinite groups. We show that any sorted profinite group has a universal SEP-cover. Our proof gives an alternative proof for the existence of a universal embedding cover of a profinite group. Also our proof works for any full subcategory of the sorted profinite groups, which is closed under taking finite quotients, fibre products, and inverse limits. We also show that any sorted profinite group having SEP has a sorted complete system whose theory is $\omega $-categorical and $\omega $-stable under the assumption that the set of sorts is countable.

Keywords

sorted profinite groupssorted complete systemsorted embedding propertyco-sorted embedding propertysorted embedding cover

MSC classification

Primary: 03C60: Model-theoretic algebra
Secondary: 08C10: Axiomatic model classes
Type
Article
Information
The Journal of Symbolic Logic , Volume 88 , Issue 3 , September 2023 , pp. 1005 - 1037
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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