A descending chain condition for groups definable in o-minimal structures

Alessandro Berarducci, Margarita Otero, Yaa'cov Peterzil, Anand Pillay

Research output: Contribution to journalArticlepeer-review


We prove that if G is a group definable in a saturated o-minimal structure, then G has no infinite descending chain of type-definable subgroups of bounded index. Equivalently, G has a smallest (necessarily normal) type-definable subgroup G00 of bounded index and G/G00 equipped with the "logic topology" is a compact Lie group. These results give partial answers to some conjectures of the fourth author.

Original languageEnglish
Pages (from-to)303-313
Number of pages11
JournalAnnals of Pure and Applied Logic
Issue number2-3
StatePublished - Jul 2005

Bibliographical note

Funding Information:
The first two authors thank Dikran Dikranjan for useful information on compact groups. M. Otero was partially supported by BFM-2002-04797. Y. Peterzil was partially supported by funds from the NSF Focused Research Grant DMS-0100979. A. Pillay was partially supported by NSF grants DMS-0300639 and the FRG DMS-0100979.


  • Compact groups
  • Descending chain conditions
  • Type-definable subgroups
  • o-minimality

ASJC Scopus subject areas

  • Logic


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