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Preprint Number 703

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703. John Goodrick, Byunghan Kim, and Alexei Kolesnikov
Type-amalgamation properties and polygroupoids in stable theories
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Submission date: 5 April 2014.

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).

Mathematics Subject Classification: 03C45

Keywords and phrases:

Full text arXiv 1404.1525: pdf, ps.


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