### Toward classifying unstable theories

by Shelah. [Sh:500]

Annals Pure and Applied Logic, 1996

The paper deals with two issues: the existence of
universal models of a theory T and related properties when
cardinal arithmetic does not give this existence offhand. In the
first section we prove that simple theories (e.g., theories
without the tree property, a class properly containing the
stable theories) behaves ``better'' than theories with the
strict order property, by criterion from [Sh:457]. In the
second section we introduce properties SOP_n such that the
strict order property implies SOP_{n+1}, which implies
SOP_n, which in turn implies the tree property. Now SOP_4
already implies non-existence of universal models in cases where
earlier the strict order property was needed, and SOP_3
implies maximality in the Keisler order, again improving an
earlier result which had used the strict order property.

Back to the list of publications