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Definability of groups in $\aleph_0$-stable metric structures
- Source :
- J. Symbolic Logic 75, 3 (2010) 817-840
- Publication Year :
- 2008
-
Abstract
- We prove that in a continuous $\aleph_0$-stable theory every type-definable group is definable. The two main ingredients in the proof are: \begin{enumerate} \item Results concerning Morley ranks (i.e., Cantor-Bendixson ranks) from \cite{BenYaacov:TopometricSpacesAndPerturbations}, allowing us to prove the theorem in case the metric is invariant under the group action; and \item Results concerning the existence of translation-invariant definable metrics on type-definable groups and the extension of partial definable metrics to total ones. \end{enumerate}
- Subjects :
- Mathematics - Logic
03C45, 03C90
Subjects
Details
- Database :
- arXiv
- Journal :
- J. Symbolic Logic 75, 3 (2010) 817-840
- Publication Type :
- Report
- Accession number :
- edsarx.0802.4286
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.2178/jsl/1278682202