A classification of 2-chains having 1-shell boundaries in rosy theories
Logic
2015-03-17 v1
Abstract
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 -chains whose boundary is a -shell.
Keywords
Cite
@article{arxiv.1503.04564,
title = {A classification of 2-chains having 1-shell boundaries in rosy theories},
author = {Byunghan Kim and SunYoung Kim and Junguk Lee},
journal= {arXiv preprint arXiv:1503.04564},
year = {2015}
}
Comments
22 pages with 1 figure, To be published in Journal of Symbolic Logic