Small extensions of models of o-minimal theories and absolute homogeneity

2008

Closed access Metadata (CSL-JSON)
DOI 10.3103/s1055134408020053
Data confidence 70 medium
How this score is calculated

It is built from checkable properties of the record itself: whether the article has a DOI, how many independent sources confirmed its data, whether the required fields are filled in, and how recent the latest confirmation is. Disagreement between sources and a missing identifier lower it. A value of 80 or above means the record was published without further checking; 60 to 79 means it is published at reduced confidence, with a manual check advisable. A record verified by an editor by hand is never pushed below 90 by a recalculation. This scores our data about the article, not the article itself.

Abstract

We obtain some results on existence of small extensions of models of weakly o -minimal atomic theories. In particular, we find a sharp upper estimate for the Hanf number of such a theory for omitting an arbitrary family of pure types. We also find a sharp upper estimate for cardinalities of weakly o -minimal absolutely homogeneous models and a sufficient condition for absolute homogeneity.