Ordering Free Products in Reverse Mathematics

This paper is a contribution to Harvey Friedman’s project of reverse mathematics in which one tries to classify theorems of ordinary mathematics by the set theoretic axioms required to prove them. All of the result in this paper are formalized in RCA0, the weakest of the standard systems in reverse mathematics, and concern classical theorems about countable ordered groups. The reader who is not familiar with reverse mathematics is referred to Simpson [8] for the background definitions and to Solomon [9] and [10] for specific information concerning reverse mathematics and ordered groups. We begin with some background definitions before stating our main results.