Maximal small extensions of o‐minimal structures |
| |
| Authors: | Janak Ramakrishnan |
| |
| Affiliation: | Institut Camille Jordan, Université Claude Bernard Lyon 1, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne cedex, France |
| |
| 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 (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
| |
| Keywords: | o‐minimality small extension |
|
|
