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. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Pastori, E., Spiga, P. (2011). Failure of n-uniqueness: A family of examples. MATHEMATICAL LOGIC QUARTERLY, 57(2), 133-148 [10.1002/malq.200910127].
Failure of n-uniqueness: A family of examples
SPIGA, PABLOUltimo
2011
Abstract
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. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
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