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Mathematics > Logic

arXiv:1804.09067 (math)
[Submitted on 24 Apr 2018 (v1), last revised 17 May 2019 (this version, v3)]

Title:Categoricity in multiuniversal classes

Authors:Nathanael Ackerman, Will Boney, Sebastien Vasey
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Abstract:The third author has shown that Shelah's eventual categoricity conjecture holds in universal classes: class of structures closed under isomorphisms, substructures, and unions of chains. We extend this result to the framework of multiuniversal classes. Roughly speaking, these are classes with a closure operator that is essentially algebraic closure (instead of, in the universal case, being essentially definable closure). Along the way, we prove in particular that Galois (orbital) types in multiuniversal classes are determined by their finite restrictions, generalizing a result of the second author.
Comments: 15 pages
Subjects: Logic (math.LO)
MSC classes: 03C48 (Primary), 03C45, 03C52, 03C55, 03C75 (Secondary)
Cite as: arXiv:1804.09067 [math.LO]
  (or arXiv:1804.09067v3 [math.LO] for this version)
  https://doi.org/10.48550/arXiv.1804.09067

Submission history

From: Sebastien Vasey [view email]
[v1] Tue, 24 Apr 2018 14:32:38 UTC (22 KB)
[v2] Tue, 15 May 2018 14:21:48 UTC (24 KB)
[v3] Fri, 17 May 2019 13:11:48 UTC (20 KB)
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