### 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 |

Editors | Xishun Zhao, Qi Feng, Byunghan Kim, Liang Yu |

Publisher | World Scientific Publishing Co. Pte Ltd |

Pages | 93-104 |

Number of pages | 12 |

ISBN (Print) | 9789814675994 |

DOIs | |

Publication status | Published - 2013 |

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

### Publication series

Name | Proceedings of the 13th Asian Logic Conference, ALC 2013 |
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### 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

Goodrick, J., Kim, B., & Kolesnikov, A. (2013). Characterization of the second homology group of a stationary type in a stable theory. In X. Zhao, Q. Feng, B. Kim, & L. Yu (Eds.),

*Proceedings of the 13th Asian Logic Conference, ALC 2013*(pp. 93-104). (Proceedings of the 13th Asian Logic Conference, ALC 2013). World Scientific Publishing Co. Pte Ltd. https://doi.org/10.1142/9789814678001_0005