Homology groups of types in stable theories and the Hurewicz correspondence

John Goodrick, Byunghan Kim, Alexei Kolesnikov

Research output: Contribution to journalArticlepeer-review

2 Citations (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

Bibliographical note

Funding Information:
The second author was supported by NRF of Korea grant 2013R1A1A2073702, and Samsung Science Technology Foundation under Project Number SSTF-BA1301-03.

Publisher Copyright:
© 2017 Elsevier B.V.

All Science Journal Classification (ASJC) codes

  • Logic

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