Homology groups of types in stable theories and the Hurewicz correspondence

2014/12/11 by John Goodrick, Goodrick, John, Byunghan Kim +3
Mathematics · #03C45 #Advanced Topology and Set Theory #FOS: Mathematics #Logic (math.LO) #math.LO #msc:03C45

paper · pdf · doi:10.48550/arxiv.1412.3864

24 pages

openalex publication_date 2014/12/11 · arxiv created 2016/09/11 · arxiv updated 2016/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an explicit description of the homomorphism group H_n(p) of a strong type p in any stable theory under the assumption that for every non-forking extension q of p the groups H_i(q) are trivial for i at least 2 but less than n. The group H_n(p) turns out to be isomorphic to the automorphism group of a certain piece of the algebraic closure of n independent realizations of p; it was shown earlier by the authors that such a group must be abelian. We call this the "Hurewicz correspondence" in analogy with the Hurewicz Theorem in algebraic topology.

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