Type-amalgamation properties and polygroupoids in stable theories
Logic
2014-04-08 v1
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).
Cite
@article{arxiv.1404.1525,
title = {Type-amalgamation properties and polygroupoids in stable theories},
author = {John Goodrick and Byunghan Kim and Alexei Kolesnikov},
journal= {arXiv preprint arXiv:1404.1525},
year = {2014}
}
Comments
37 pages