Homology groups of types in stable theories and the Hurewicz correspondence

John Goodrick, Byunghan Kim, Alexei Kolesnikov

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We give an explicit description of the homology group Hn(p) of a strong type p in any stable theory under the assumption that for every non-forking extension q of p the groups Hi(q) are trivial for 2≤i<n. The group Hn(p) turns out to be isomorphic to the automorphism group of a certain part of the algebraic closure of n independent realizations of p; it follows from the authors’ earlier work that such a group must be abelian. We call this the “Hurewicz correspondence” by analogy with the Hurewicz Theorem in algebraic topology.

Original languageEnglish
Pages (from-to)1710-1728
Number of pages19
JournalAnnals of Pure and Applied Logic
Volume168
Issue number9
DOIs
Publication statusPublished - 2017 Sep 1

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Homology Groups
Correspondence
Algebraic topology
P-groups
Automorphism Group
Analogy
Trivial
Closure
Isomorphic
Theorem

All Science Journal Classification (ASJC) codes

  • Logic

Cite this

Goodrick, John ; Kim, Byunghan ; Kolesnikov, Alexei. / Homology groups of types in stable theories and the Hurewicz correspondence. In: Annals of Pure and Applied Logic. 2017 ; Vol. 168, No. 9. pp. 1710-1728.
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Homology groups of types in stable theories and the Hurewicz correspondence. / Goodrick, John; Kim, Byunghan; Kolesnikov, Alexei.

In: Annals of Pure and Applied Logic, Vol. 168, No. 9, 01.09.2017, p. 1710-1728.

Research output: Contribution to journalArticle

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