Failure of n-uniqueness: a family of examples

✍ Scribed by Elisabetta Pastori; Pablo Spiga

• Book ID: 102487145
• Publisher: John Wiley and Sons
• Year: 2011
• Tongue: English
• Weight: 200 KB
• Volume: 57
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.200910127

✦ Synopsis

In this paper, the connections between model theory and the theory of infinite permutation groups (see [11]) are used to study the n-existence and the n-uniqueness for n-amalgamation problems of stable theories. We show that, for any n ≥ 2, there exists a stable theory having (k + 1)-existence and k-uniqueness, for every k ≤ n, but has neither (n + 2)-existence nor (n + 1)-uniqueness. In particular, this generalizes the example, for n = 2, due to Hrushovski given in [3].