A CLASSIFICATION OF 2-CHAINS HAVING 1-SHELL BOUNDARIES IN ROSY THEORIES

@article{Kim2015ACO,
  title={A CLASSIFICATION OF 2-CHAINS HAVING 1-SHELL BOUNDARIES IN ROSY THEORIES},
  author={Byunghan Kim and Sunyoung Kim and Junguk Lee},
  journal={The Journal of Symbolic Logic},
  year={2015},
  volume={80},
  pages={322 - 340}
}
Abstract We classify, in a nontrivial 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. 
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More on classification of 2-chains having 1-shell boundaries in rosy theories, preprint. DEPARTMENT OF MATHEMATICS YONSEI UNIVERSITY 50 YONSEI-RO
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    More on classification of 2-chains having 1-shell boundaries in rosy theories. Preprint. Department of Mathematics, Yonsei University, 50 Yonsei-Ro, Seodaemun- Gu, Seoul 120-749, Korea E-mail address
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