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Preprint Number 259
259. Elisabetta Pastori and Pablo Spiga
Failure on n-uniqueness: a family of examples
Submission date: 2 July 2010.
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.
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