A classification of 2-chains having 1-shell boundaries in rosy theories [article]

Byunghan Kim, SunYoung Kim, Junguk Lee
2015 arXiv   pre-print
We classify, in a non-trivial amenable collection of functors, all 2-chains up to the relation of having the same 1-shell boundary. In particular, we prove that in a rosy theory, every 1-shell of a Lascar strong type is the boundary of some 2-chain, hence making the 1st homology group trivial. We also show that, unlike in simple theories, in rosy theories there is no upper bound on the minimal lengths of 2-chains whose boundary is a 1-shell.
arXiv:1503.04564v1 fatcat:k46r7whptfeudbcoilljeetpdm