Interpreting groups inside modular strongly minimal homogeneous models

Journal of Mathematical Logic 3 (01):127-142 (2003)
  Copy   BIBTEX

Abstract

A large homogeneous model M is strongly minimal, if any definable subset is either bounded or has bounded complement. In this case is a pregeometry, where bcl denotes the bounded closure operation. In this paper, we show that if M is a large homogeneous strongly minimal structure and is non-trivial and locally modular, then M interprets a group. In addition, we give a description of such groups.

Categories

Keywords

Reprint years

DOI

10.1142/s0219061303000200

Other Versions

No versions found

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 100,865

External links

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

Through your library

My notes

Similar books and articles

Locally modular geometries in homogeneous structures.Tapani Hyttinen - 2005 - Mathematical Logic Quarterly 51 (3):291.
Automorphism groups of trivial strongly minimal structures.Thomas Blossier - 2003 - Journal of Symbolic Logic 68 (2):644-668.
Weakly minimal groups with a new predicate.Gabriel Conant & Michael C. Laskowski - 2020 - Journal of Mathematical Logic 20 (2):2050011.
One theorem of Zil′ber's on strongly minimal sets.Steven Buechler - 1985 - Journal of Symbolic Logic 50 (4):1054-1061.
Definable group extensions in semi‐bounded o‐minimal structures.Mário J. Edmundo & Pantelis E. Eleftheriou - 2009 - Mathematical Logic Quarterly 55 (6):598-604.
Definable Tietze extension property in o-minimal expansions of ordered groups.Masato Fujita - 2023 - Archive for Mathematical Logic 62 (7):941-945.
Type-Definable and Invariant Groups in O-Minimal Structures.Jana Maříková - 2007 - Journal of Symbolic Logic 72 (1):67 - 80.
Definable completeness of P-minimal fields and applications.Pablo Cubides Kovacsics & Françoise Delon - 2022 - Journal of Mathematical Logic 22 (2).
On Nonstructure of Elementary Submodels of an Unsuperstable Homogeneous Structure.Tapani Hyttinen - 1997 - Mathematical Logic Quarterly 43 (1):134-142.
Type-definability, compact lie groups, and o-minimality.Anand Pillay - 2004 - Journal of Mathematical Logic 4 (02):147-162.

Analytics

Added to PP
2012-09-02

Downloads
17 (#1,147,714)

6 months
8 (#575,465)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

Strong splitting in stable homogeneous models.Tapani Hyttinen & Saharon Shelah - 2000 - Annals of Pure and Applied Logic 103 (1-3):201-228.
Minimale Gruppen.Joachim Reineke - 1975 - Mathematical Logic Quarterly 21 (1):357-359.
Almost orthogonal regular types.Ehud Hrushovski - 1989 - Annals of Pure and Applied Logic 45 (2):139-155.
Canonical Finite Diagrams and Quantifier Elimination.Tapani Hyttinen - 2002 - Mathematical Logic Quarterly 48 (4):533-554.

Add more references