### 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) |
---|---|

Pages (from-to) | 2752-2763 |

Number of pages | 12 |

Journal | Communications in Algebra |

Volume | 39 |

Issue number | 8 |

DOIs | |

State | Published - Aug 1 2011 |

### Fingerprint

### Keywords

- Definability
- Mann pairs
- Model theory

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Communications in Algebra*,

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

**Definable sets in Mann pairs.** / van den Dries, Lou; Günaydin, Ayhan.

Research output: Contribution to journal › Article

*Communications in Algebra*, vol. 39, no. 8, pp. 2752-2763. https://doi.org/10.1080/00927872.2010.489919

}

TY - JOUR

T1 - Definable sets in Mann pairs

AU - van den Dries, Lou

AU - Günaydin, Ayhan

PY - 2011/8/1

Y1 - 2011/8/1

N2 - 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 ωn that are definable in (ω,k,γ).

AB - 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 ωn that are definable in (ω,k,γ).

KW - Definability

KW - Mann pairs

KW - Model theory

UR - http://www.scopus.com/inward/record.url?scp=80051813609&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80051813609&partnerID=8YFLogxK

U2 - 10.1080/00927872.2010.489919

DO - 10.1080/00927872.2010.489919

M3 - Article

AN - SCOPUS:80051813609

VL - 39

SP - 2752

EP - 2763

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 8

ER -