# 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}
}
• Published 1 March 2015
• Mathematics
• The Journal of Symbolic Logic
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.
6 Citations
More on 2-chains with 1-shell boundaries in rosy theories
• Mathematics
• 2017
In [4], B. Kim, and the authors classified 2-chains with 1shell boundaries into either RN (renamable)-type or NR (non renamable)-type 2-chains up to renamability of support of subsummands of a
Lascar groups and the first homology groups of strong types in rosy theories
For a rosy theory, we give a canonical surjective homomorphism from a Lascar group over $A=\acl^{eq}(A)$ to a first homology group of a strong type over $A$, and we describe its kernel by an
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THE RELATIVIZED LASCAR GROUPS, TYPE-AMALGAMATION, AND ALGEBRAICITY
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• 2021
It is proved a purely compact group-theoretic result that any compact connected abelian group is isomorphic to its quotient by every finite subgroup.
Homology Groups of Types in Model Theory and the Computation of H 2(p)
• Mathematics
The Journal of Symbolic Logic
• 2013
It is shown that if the generalized amalgamation properties hold, then the homology groups are trivial, and any profinite abelian group can occur as the group H 2 (p).

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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
• 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