Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-13T04:37:27.788Z Has data issue: false hasContentIssue false
  • English
  • Français

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: sy831@yonsei.ac.kr
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Adler, Hans, Explanations of Independence, Ph. D. Thesis, University of Freiburg, 2005.Google Scholar
Casanovas, Enrique, Lascar, Daniel, Pillay, Anand, and Ziegler, Martin, Galois groups of first order theories. Journal of Mathematical Logic, vol. 1 (2001), pp. 305–319.Google Scholar
Diestel, Reinhard, Graph Theory, 2nd ed., Springer, New York, 2000.Google Scholar
Ealy, Clifton and Onshuus, Alf, Characterizing rosy theories, this Journal, vol. 72 (2007), pp. 919–940.Google Scholar
Goodrick, John, Kim, Byunghan, and Kolesnikov, Alexei, Homology groups of types in model theory and the computation of H 2 (p), this Journal, vol. 78 (2013), pp. 1086–1114.Google Scholar
Goodrick, John, Kim, Byunghan, and Kolesnikov, Alexei, Amalgamation functors and homology groups in model theory. Proceedings of ICM 2014, to appear.Google Scholar
Kim, SunYoung and Lee, Junguk, More on classification of 2-chains having 1-shell boundaries in rosy theories, preprint.Google Scholar