Definable homomorphisms of abelian groups in o-minimal structures

&
Annals of Pure and Applied Logic 101 (1):1-27 (1999)
  Copy   BIBTEX

Abstract

We investigate the group of definable homomorphisms between two definable abelian groups A and B, in an o-minimal structure . We prove the existence of a “large”, definable subgroup of . If contains an infinite definable set of homomorphisms then some definable subgroup of B admits a definable multiplication, making it into a field. As we show, all of this can be carried out not only in the underlying structure but also in any structure definable in

Categories

Keywords

Reprint years

DOI

10.1016/s0168-0072(99)00016-0

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,219

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

Quasi-o-minimal structures.Oleg Belegradek, Ya'acov Peterzil & Frank Wagner - 2000 - Journal of Symbolic Logic 65 (3):1115-1132.
Compact domination for groups definable in linear o-minimal structures.Pantelis E. Eleftheriou - 2009 - Archive for Mathematical Logic 48 (7):607-623.
Definable Open Sets As Finite Unions of Definable Open Cells.Simon Andrews - 2010 - Notre Dame Journal of Formal Logic 51 (2):247-251.
Invariance results for definable extensions of groups.Mário J. Edmundo, Gareth O. Jones & Nicholas J. Peatfield - 2011 - Archive for Mathematical Logic 50 (1-2):19-31.
On dp-minimal ordered structures.Pierre Simon - 2011 - Journal of Symbolic Logic 76 (2):448 - 460.
Topological properties of sets definable in weakly o-minimal structures.Roman Wencel - 2010 - Journal of Symbolic Logic 75 (3):841-867.
A remark on divisibility of definable groups.Mário J. Edmundo - 2005 - Mathematical Logic Quarterly 51 (6):639-641.
Strongly and co-strongly minimal abelian structures.Ehud Hrushovski & James Loveys - 2010 - Journal of Symbolic Logic 75 (2):442-458.
Type-Definable and Invariant Groups in O-Minimal Structures.Jana Maříková - 2007 - Journal of Symbolic Logic 72 (1):67 - 80.
Groups definable in linear o-minimal structures: the non-compact case.Pantelis E. Eleftheriou - 2010 - Journal of Symbolic Logic 75 (1):208-220.
Splitting definably compact groups in o-minimal structures.Marcello Mamino - 2011 - Journal of Symbolic Logic 76 (3):973 - 986.
The universal covering homomorphism in o‐minimal expansions of groups.Mário J. Edmundo & Pantelis E. Eleftheriou - 2007 - Mathematical Logic Quarterly 53 (6):571-582.
Non-standard lattices and o-minimal groups.Pantelis E. Eleftheriou - 2013 - Bulletin of Symbolic Logic 19 (1):56-76.
Boolean Skeletons of MV-algebras and ℓ-groups.Roberto Cignoli - 2011 - Studia Logica 98 (1-2):141-147.
Vapnik–Chervonenkis Density in Some Theories without the Independence Property, II.Matthias Aschenbrenner, Alf Dolich, Deirdre Haskell, Dugald Macpherson & Sergei Starchenko - 2013 - Notre Dame Journal of Formal Logic 54 (3-4):311-363.

Analytics

Added to PP
2014-01-16

Downloads
33 (#459,370)

6 months
3 (#902,269)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Definably compact Abelian groups.Mário J. Edmundo & Margarita Otero - 2004 - Journal of Mathematical Logic 4 (02):163-180.
Locally definable homotopy.Elías Baro & Margarita Otero - 2010 - Annals of Pure and Applied Logic 161 (4):488-503.
A remark on divisibility of definable groups.Mário J. Edmundo - 2005 - Mathematical Logic Quarterly 51 (6):639-641.
Connected components of definable groups, and o-minimality II.Annalisa Conversano & Anand Pillay - 2015 - Annals of Pure and Applied Logic 166 (7-8):836-849.

View all 16 citations / Add more citations

References found in this work

No references found.

Add more references