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Preprint Number 846
846. Byunghan Kim, SunYoung Kim, and Junguk Lee
A classification of 2-chains having 1-shell boundaries in rosy theories
Submission date: 16 March 2015.
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.
Mathematics Subject Classification: 03C45
Keywords and phrases: rosy theories, homology groups, 2-chains having a 1-shell boundary, CR/RS-operations, RN/NR-type 2-chains
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