English

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 22-chains whose boundary is a 11-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