Submission date: 2 July 2010.

Abstract:

In this paper, the connections between model theory and the theory of infinite permutation groups are used to study the n-existence and the n-uniqueness for n-amalgamation problems of stable theories. We show that, for any n>1, there exists a stable theory having (k+1)-existence and k-uniqueness, for every k< n+1, but has neither (n+2)-existence nor (n+1)-uniqueness. In particular, this generalizes the example, for n=2, due to E.Hrushovski.

Mathematics Subject Classification: 03C45, 03C50, 20B27

Keywords and phrases: Higher Amalgamation Properties, Stable Theories, Infinite Permutation Groups.

Full text arXiv: pdf, ps.