Submission date: 24 June 2010.

Abstract:

This paper continues the study of generalized amalgamation properties. Part of the paper provides a finer analysis of the groupoids that arise from failure of 3-uniqueness in a stable theory. We show that such groupoids must be abelian and link the binding group of the groupoids to a certain automorphism group of the monster model, showing that the group must be abelian as well. We also introduce generalized n-existence and n-uniqueness properties (the “boundary properties”) in the context of simple theories and investigate connections between the various properties. Finally, we give examples of first-order simple unstable theories showing, in particular, that there is no straightforward generalization of the groupoid construction in an unstable context.

Mathematics Subject Classification: 03C45

Keywords and phrases: Amalgamation functors and boundary properties in simple theories.

Full text arXiv: pdf, ps.