Ibrahim Mohammed (University of Leeds)

In the paper "Abelian Groups with Contractions", F.V Kuhlmann introduced the notion of contraction group. They consist of an ordered abelian group along with a unary map which collapses archimedean classes to a single point. The motivation behind them was to axiomatise the action of log on the value group of a non-standard model of $\mathbb{R}_{\text{exp}}$, however there are a few other natural ways in which contraction groups arise.

The first is the action of a hyper-logarithm (which can be thought of the composition of log $\omega$ many times) on the value group of a trans-exponential ordered field. The other is the action of the hyper-logaithmic derivative on the same structure. In this talk I'll go through how contraction groups arise in these circumstances, and state various model theoretic results concerning them.