Definable homomorphisms of abelian groups in o-minimal structures

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

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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.

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