Type-amalgamation properties and polygroupoids in stable theories

Journal of Mathematical Logic 15 (1):1550004 (2015)
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We show that in a stable first-order theory, the failure of higher dimensional type amalgamation can always be witnessed by algebraic structures that we call n-ary polygroupoids. This generalizes a result of Hrushovski in [16] that failures of 4-amalgamation are witnessed by definable groupoids. The n-ary polygroupoids are definable in a mild expansion of the language.



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Citations of this work

Disjoint $n$ -Amalgamation and Pseudofinite Countably Categorical Theories.Alex Kruckman - 2019 - Notre Dame Journal of Formal Logic 60 (1):139-160.
On the n-uniqueness of types in rosy theories.Byunghan Kim - 2016 - Archive for Mathematical Logic 55 (5-6):677-686.

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References found in this work

Classification Theory and the Number of Nonisomorphic Models.S. Shelah - 1982 - Journal of Symbolic Logic 47 (3):694-696.
Generalized amalgamation and n -simplicity.Byunghan Kim, Alexei S. Kolesnikov & Akito Tsuboi - 2008 - Annals of Pure and Applied Logic 155 (2):97-114.
Failure of n -uniqueness: a family of examples.Elisabetta Pastori & Pablo Spiga - 2011 - Mathematical Logic Quarterly 57 (2):133-148.

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