### 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 H_{2}(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 H_{2}(p) ≅ G.

Original language | English |
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Title of host publication | Proceedings of the 13th Asian Logic Conference, ALC 2013 |

Publisher | World Scientific Publishing Co. Pte Ltd |

Pages | 93-104 |

Number of pages | 12 |

ISBN (Print) | 9789814675994 |

Publication status | Published - 2013 Jan 1 |

Event | 13th Asian Logic Conference, ALC 2013 - Guangzhou, China Duration: 2013 Sep 16 → 2013 Sep 20 |

### Other

Other | 13th Asian Logic Conference, ALC 2013 |
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Country | China |

City | Guangzhou |

Period | 13/9/16 → 13/9/20 |

### All Science Journal Classification (ASJC) codes

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

### Cite this

*Proceedings of the 13th Asian Logic Conference, ALC 2013*(pp. 93-104). World Scientific Publishing Co. Pte Ltd.

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*Proceedings of the 13th Asian Logic Conference, ALC 2013.*World Scientific Publishing Co. Pte Ltd, pp. 93-104, 13th Asian Logic Conference, ALC 2013, Guangzhou, China, 13/9/16.

**Characterization of the second homology group of a stationary type in a stable theory.** / Goodrick, John; Kim, Byunghan; Kolesnikov, Alexei.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Characterization of the second homology group of a stationary type in a stable theory

AU - Goodrick, John

AU - Kim, Byunghan

AU - Kolesnikov, Alexei

PY - 2013/1/1

Y1 - 2013/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85007357394&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85007357394&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:85007357394

SN - 9789814675994

SP - 93

EP - 104

BT - Proceedings of the 13th Asian Logic Conference, ALC 2013

PB - World Scientific Publishing Co. Pte Ltd

ER -