Definable homomorphisms of abelian groups in o-minimal structures

Ya'acov Peterzil, Sergei Starchenko

Research output: Contribution to journalArticlepeer-review


We investigate the group ℋ of definable homomorphisms between two definable abelian groups A and B, in an o-minimal structure script N. We prove the existence of a "large", definable subgroup of ℋ. If ℋ contains an infinite definable set of homomorphisms then some definable subgroup of B (equivalently, a definable quotient of A) 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 script N but also in any structure definable in script N.

Original languageEnglish
Pages (from-to)1-27
Number of pages27
JournalAnnals of Pure and Applied Logic
Issue number1
StatePublished - 15 Nov 1999

Bibliographical note

Funding Information:
E-mail addresses: (Y. Peterzil), (S. Starchenko) 1The second author was partially supported by NSF.


  • Definably compact groups
  • o-minimal structures

ASJC Scopus subject areas

  • Logic


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