Maximal small extensions of o-minimal structures

Details Maximal small extensions of o-minimal structures Maximal small extensions of o-minimal structures

2007-12-04

arxiv.org/abs/0712.0591v3

Mathematics

Logic

6 pages. To appear in Mathematical Logic Quarterly

Scientific paper

10.1002/malq.200910102

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.

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