Type-amalgamation properties and polygroupoids in stable theories
Journal of Mathematical Logic 15 (1):1550004 (2015)
Abstract
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.DOI
10.1142/s021906131550004x
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Citations of this work
Homology groups of types in stable theories and the Hurewicz correspondence.John Goodrick, Byunghan Kim & Alexei Kolesnikov - 2017 - Annals of Pure and Applied Logic 168 (9):1710-1728.
Induced and higher-dimensional stable independence.Michael Lieberman, Jiří Rosický & Sebastien Vasey - 2022 - Annals of Pure and Applied Logic 173 (7):103124.
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.
References found in this work
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Constructing the hyperdefinable group from the group configuration.Tristram de Piro, Byunghan Kim & Jessica Millar - 2006 - Journal of Mathematical Logic 6 (2):121-139.
Generalized amalgamation and n -simplicity.Byunghan Kim, Alexei S. Kolesnikov & Akito Tsuboi - 2008 - Annals of Pure and Applied Logic 155 (2):97-114.
Groupoids, covers, and 3-uniqueness in stable theories.John Goodrick & Alexei Kolesnikov - 2010 - Journal of Symbolic Logic 75 (3):905-929.
Failure of n -uniqueness: a family of examples.Elisabetta Pastori & Pablo Spiga - 2011 - Mathematical Logic Quarterly 57 (2):133-148.
