Characterization of the second homology group of a stationary type in a stable theory

John Goodrick, Byunghan Kim, Alexei Kolesnikov

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Let T be a stable theory. It was shown in Ref. 5 that one can define the notions of homology groups attached to a stationary type of T. It was also shown that if T fails to have an amalgamation property called 3-uniqueness, then for some stationary type p the homology group H2(p) has to be a nontrivial abelian profinite group. The goal of this paper is to show that for any abelian profinite group G there is a stable (in fact, categorical) theory and a stationary type p such that H2(p) ≅ G.

Original languageEnglish
Title of host publicationProceedings of the 13th Asian Logic Conference, ALC 2013
EditorsQi Feng, Xishun Zhao, Liang Yu, Byunghan Kim
PublisherWorld Scientific Publishing Co. Pte Ltd
Pages93-104
Number of pages12
ISBN (Print)9789814675994
Publication statusPublished - 2013 Jan 1
Event13th Asian Logic Conference, ALC 2013 - Guangzhou, China
Duration: 2013 Sep 162013 Sep 20

Publication series

NameProceedings of the 13th Asian Logic Conference, ALC 2013

Other

Other13th Asian Logic Conference, ALC 2013
CountryChina
CityGuangzhou
Period13/9/1613/9/20

All Science Journal Classification (ASJC) codes

  • Hardware and Architecture
  • Computer Vision and Pattern Recognition
  • Computational Theory and Mathematics

Cite this

Goodrick, J., Kim, B., & Kolesnikov, A. (2013). Characterization of the second homology group of a stationary type in a stable theory. In Q. Feng, X. Zhao, L. Yu, & B. Kim (Eds.), Proceedings of the 13th Asian Logic Conference, ALC 2013 (pp. 93-104). (Proceedings of the 13th Asian Logic Conference, ALC 2013). World Scientific Publishing Co. Pte Ltd.