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Mathematics > Logic

arXiv:0712.0591 (math)
[Submitted on 4 Dec 2007 (v1), last revised 30 Mar 2010 (this version, v3)]

Title:Maximal small extensions of o-minimal structures

Authors:Janak Ramakrishnan
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Abstract:A proper elementary extension of a model is called small if it realizes no new types over any finite set in the base model. We answer a question of Marker, and show that it is possible to have an o-minimal structure with a maximal small extension. Our construction yields such a structure for any cardinality. We show that in some cases, notably when the base structure is countable, the maximal small extension has maximal possible cardinality.
Comments: 6 pages. To appear in Mathematical Logic Quarterly
Subjects: Logic (math.LO)
MSC classes: 03C64 (Primary), 03C45 (Secondary), 03C50
Cite as: arXiv:0712.0591 [math.LO]
  (or arXiv:0712.0591v3 [math.LO] for this version)
  https://doi.org/10.48550/arXiv.0712.0591
Related DOI: https://doi.org/10.1002/malq.200910102

Submission history

From: Janak Ramakrishnan [view email]
[v1] Tue, 4 Dec 2007 19:24:32 UTC (6 KB)
[v2] Sun, 6 Sep 2009 13:39:40 UTC (7 KB)
[v3] Tue, 30 Mar 2010 12:56:05 UTC (8 KB)
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