## Journal of Symbolic Logic

### Type-definable and invariant groups in o-minimal structures

Jana Maříková

#### Abstract

Let $M$ be a big o-minimal structure and $G$ a type-definable group in $M^n$. We show that $G$ is a type-definable subset of a definable manifold in $M^n$ that induces on $G$ a group topology. If $M$ is an o-minimal expansion of a real closed field, then $G$ with this group topology is even definably isomorphic to a type-definable group in some $M^k$ with the topology induced by $M^k$. Part of this result holds for the wider class of so-called invariant groups: each invariant group $G$ in $M^n$ has a unique topology making it a topological group and inducing the same topology on a large invariant subset of the group as $M^n$.

#### Article information

Source
J. Symbolic Logic, Volume 72, Issue 1 (2007), 67-80.

Dates
First available in Project Euclid: 23 March 2007

https://projecteuclid.org/euclid.jsl/1174668384

Digital Object Identifier
doi:10.2178/jsl/1174668384

Mathematical Reviews number (MathSciNet)
MR2298471

Zentralblatt MATH identifier
1118.03028

#### Citation

Maříková, Jana. Type-definable and invariant groups in o-minimal structures. J. Symbolic Logic 72 (2007), no. 1, 67--80. doi:10.2178/jsl/1174668384. https://projecteuclid.org/euclid.jsl/1174668384