High and Low Homogeneity

2021

Closed access Metadata (CSL-JSON)
DOI 10.1134/s1055134421010028
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 find conditions such that every $$\lambda $$ -homogeneous model with small $$ \lambda $$ satisfying these conditions is homogeneous. As a corollary, we obtain conditions guaranteeing that the following implication holds: If $$T $$ is a theory, $$\mu >|T| $$ , and every model of $$T $$ of cardinality $$ \mu $$ is $$\omega _1$$ -homogeneous then every model of $$T$$ of sufficiently large cardinality is homogeneous.