### Abstract

Consider structures (ω,k,γ) where ω is an algebraically closed field of characteristic zero, k is a subfield, and γ is a subgroup of the multiplicative group of ω. Certain pairs (k,γ) have been singled out as Mann pairs in [4]. We give new examples of such Mann pairs, we axiomatize for each Mann pair (k,γ) the first-order theory of (ω,k,γ) in a cleaner way than in [4], and, as the main result of the article, we characterize the subsets of ω^{n} that are definable in (ω,k,γ).

Original language | English (US) |
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Pages (from-to) | 2752-2763 |

Number of pages | 12 |

Journal | Communications in Algebra |

Volume | 39 |

Issue number | 8 |

DOIs | |

State | Published - Aug 1 2011 |

### Keywords

- Definability
- Mann pairs
- Model theory

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

van den Dries, L., & Günaydin, A. (2011). Definable sets in Mann pairs.

*Communications in Algebra*,*39*(8), 2752-2763. https://doi.org/10.1080/00927872.2010.489919