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

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 $2$-chains whose boundary is a $1$-shell.

22 pages with 1 figure, To be published in Journal of Symbolic Logic

References in corpus (1)

• Amalgamation functors and homology groups in model theory