Salma Kuhlmann : An uncountable family of logarithmic functions with distinct growth rates. Joint Work with J.-P. Rolin

Posted by , part of the Logic Seminar.

At

March 30, 2009, 4 p.m.

In

SEO 612

Abstract

We consider a totally ordered set $\Gamma$ of cardinality $\aleph_1$, of which elements are germs at $+\infty$ of real valued functions of a real variable. We show that the order type of $\Gamma$ is that of a lexicographic ordering which admits $2^{\aleph_1}$ automorphisms of pairwise distinct orbital growth. We associate to each such automorphism a well defined logarithmic function on the field $\mathbb{R}((G))_{\aleph_1}$, where $\mathbb{R}((G))_{\aleph_1}$ is the field of generalized series with countable support, real coefficients and exponents in the group $G$ of transmonomials at $+\infty$ defined by $\Gamma$. We show that distinct automorphisms induce logarithmic functions of distinct growth rates.

seminar begins with tea.