OS Complexity Theory, Model Theory, Set Theory: Various contractions arising in Natural Ways

Montag, 27. November 2023
15:15 bis 16:45 Uhr


Veranstaltet von

Vortragende Person/Vortragende Personen:
Ibrahim Mohammed

In the paper ”Abelian Groups with Contractions”, F.V Kuhlmann introduced
the notion of contraction group. They consist of an ordered abelian group G
along with a unary map χ : G → G which collapses archimedean classes to a
single point. The motivation behind them was to axiomatise the action of log(x)
on the value group of a non-standard model of Rexp, 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(x) with itself ω 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.