Computational and Proof Theoretic Aspects of Ordered Groups
by
Reed Solomon
Victoria University and University of Wisconsin, Madison

Ordered groups provide an excellent arena for the analysis of the proof-theoretical strength of various theorems of mathematics under the Friedman-Simpson ``reverse mathematics'' programme. That is, in various subsystems of second order arithmetic, one calibtrates theorems in terms of the amount of comprehension one needs to prove the theorem. In this talk I will provide an overview of this programme using various classical theorems in the area of ordered groups as a basis. For instance, I will look at B. Neumann's Theorem showing that every countable ordered group is isomorphic to an ordered version of a free group factored out by a convex normal subgroup, Maltsev's Theorem that classifying the order types of ordered groups, and Hahn's Theorem that each countable ordered group is isomorphic to a subgroup of a Hahn Group. Naturally there are computability-theoretical corollaries. Most of the material is from my Ph. D. thesis from Cornell University.

Date received: June 23, 1998

Copyright © 1998 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cabd-64.