The classification problem for finite rank dimension groups.

摘要

There has been much work done in the study of the Borel complexity of various naturally occurring classification problems. In particular, Hjorth and Thomas have shown that the Borel complexity of the classification problem for torsion-free abelian groups of finite rank increases strictly with rank.;In this thesis, we extend this result to dimension groups of finite rank. As these groups are naturally characterized by Bratteli diagrams, we obtain a similar theorem for Bratteli diagrams. We also obtain a similar result for a class of countable simple locally finite groups which are also characterized by Bratteli diagrams.