Model theoretic connected components of finitely generated nilpotent groups

Journal of Symbolic Logic 78 (1):245-259 (2013)
  Copy   BIBTEX

Abstract

We prove that for a finitely generated infinite nilpotent group $G$ with structure $(G,\cdot,\dots)$, the connected component ${G^*}^0$ of a sufficiently saturated extension $G^*$ of $G$ exists and equals \[ \bigcap_{n\in\N} \{g^n\colon g\in G^*\}. \] We construct an expansion of ${\mathbb Z}$ by a predicate $({\mathbb Z},+,P)$ such that the type-connected component ${{\mathbb Z}^*}^{00}_{\emptyset}$ is strictly smaller than ${{\mathbb Z}^*}^0$. We generalize this to finitely generated virtually solvable groups. As a corollary of our construction we obtain an optimality result for the van der Waerden theorem for finite partitions of groups

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 90,616

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

The model theory of finitely generated finite-by-Abelian groups.Francis Oger - 1984 - Journal of Symbolic Logic 49 (4):1115-1124.
Stability of nilpotent groups of class 2 and prime exponent.Alan H. Mekler - 1981 - Journal of Symbolic Logic 46 (4):781-788.
Describing groups.André Nies - 2007 - Bulletin of Symbolic Logic 13 (3):305-339.
CM-Triviality and stable groups.Frank O. Wagner - 1998 - Journal of Symbolic Logic 63 (4):1473-1495.
A Model Theoretic Semantics for Quantum Logic.E. -W. Stachow - 1980 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1980:272 - 280.
Quasi-endomorphisms in small stable groups.Frank O. Wagner - 1993 - Journal of Symbolic Logic 58 (3):1044-1051.

Analytics

Added to PP
2013-01-24

Downloads
40 (#347,990)

6 months
2 (#670,035)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Consistency and the theory of truth.Richard Heck - 2015 - Review of Symbolic Logic 8 (3):424-466.

Add more citations

References found in this work

Type-definability, compact lie groups, and o-minimality.Anand Pillay - 2004 - Journal of Mathematical Logic 4 (02):147-162.
Galois groups of first order theories.E. Casanovas, D. Lascar, A. Pillay & M. Ziegler - 2001 - Journal of Mathematical Logic 1 (02):305-319.
G-compactness and groups.Jakub Gismatullin & Ludomir Newelski - 2008 - Archive for Mathematical Logic 47 (5):479-501.

Add more references