Cycle 30° Seminars

Place: Seminar Room "-1" -  Department of Mathematics - Via Sommarive 14 - Povo - Trento
at 11.00

• Daniel Wessel - PhD student in mathematics

Abstract:
Establishing a linear order on a group in such a way as to respect the algebraic structure in general requires a form of the axiom of choice.
However, to a certain extent this can be circumvented by concentrating on the consistency of a suitable propositional theory, rather than on the usual short but ineffective argument requiring a maximality principle.
Working with Scott’s entailment relations, we illustrate this approach by the entailment relation of positive cone of a group. In the abelian case this leads to a constructive version of Levi’s theorem that an abelian group is linearly orderable if and only if it is torsion-free.
Cederquist and Coquand’s fundamental theorem of entailment relations then prompts a finitary version of Sikora’s theorem, to which end we employ the constructive Positivstellensatz due to Coste, Lombardi, and Roy.

Supervisor: Peter Schuster