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arXiv · 1404.1525

Type-amalgamation properties and polygroupoids in stable theories

John Goodrick·Byunghan Kim·Alexei Kolesnikov
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Abstract

We show that in a stable first-order theory, the failure of higher-dimensional type amalgamation can always be witnessed by algebraic structures which we call n-ary polygroupoids. This generalizes a result of Hrushovski that failures of 4-amalgamation in stable theories are witnessed by definable groupoids (which are 2-ary polygroupoids in our terminology). The n-ary polygroupoids are definable in a mild expansion of the language (adding a unary predicate for an infinite Morley sequence).

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John Goodrick, Byunghan Kim, Alexei Kolesnikov. 2014-04-05. Type-amalgamation properties and polygroupoids in stable theories. https://arxiv.org/abs/1404.1525

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