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

Published online by Cambridge University Press:  13 March 2015

BYUNGHAN KIM ,
SUNYOUNG KIM  and
JUNGUK LEE
SUNYOUNG KIM
Affiliation:
DEPARTMENT OF MATHEMATICS, YONSEI UNIVERSITY, 50 YONSEI-RO, SEODAEMUN-GU, SEOUL 120-749, KOREAE-mail: [email protected]
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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.

Keywords

rosy theorieshomology groups2-chains having a 1-shell boundaryCR/RS-operationsRN/NR-type 2-chains
Type
Articles
Information
The Journal of Symbolic Logic , Volume 80 , Issue 1 , March 2015 , pp. 322 - 340
Copyright
Copyright © The Association for Symbolic Logic 2015 

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References

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