### Abstract

We give an explicit description of the homology 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 2≤i<n. The group H_{n}(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 language | English |
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Pages (from-to) | 1710-1728 |

Number of pages | 19 |

Journal | Annals of Pure and Applied Logic |

Volume | 168 |

Issue number | 9 |

DOIs | |

Publication status | Published - 2017 Sep 1 |

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### All Science Journal Classification (ASJC) codes

- Logic

### Cite this

*Annals of Pure and Applied Logic*,

*168*(9), 1710-1728. https://doi.org/10.1016/j.apal.2017.03.007

}

*Annals of Pure and Applied Logic*, vol. 168, no. 9, pp. 1710-1728. https://doi.org/10.1016/j.apal.2017.03.007

**Homology groups of types in stable theories and the Hurewicz correspondence.** / Goodrick, John; Kim, Byunghan; Kolesnikov, Alexei.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Homology groups of types in stable theories and the Hurewicz correspondence

AU - Goodrick, John

AU - Kim, Byunghan

AU - Kolesnikov, Alexei

PY - 2017/9/1

Y1 - 2017/9/1

N2 - 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≤in(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.

AB - 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≤in(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.

UR - http://www.scopus.com/inward/record.url?scp=85016192414&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85016192414&partnerID=8YFLogxK

U2 - 10.1016/j.apal.2017.03.007

DO - 10.1016/j.apal.2017.03.007

M3 - Article

AN - SCOPUS:85016192414

VL - 168

SP - 1710

EP - 1728

JO - Annals of Pure and Applied Logic

JF - Annals of Pure and Applied Logic

SN - 0168-0072

IS - 9

ER -