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Part I. Embedding an ordered group in a division ring. 1. Introduction. 202 2. Archimedean classification in an ordered semigroup. 204 3. Well-ordered sequences in an ordered semigroup. 4. Formal power series over a ring. 209 5. Formal power series division rings. 6. Appendix. A theorem on the group ring of a free group. Part II. Embedding the real numbers in an ordered division ring. 7. Introduction. 215 8. Preliminaries and notation. 9. Algebraic adjunction of an element. 10. Ordering a simple transcendent extension. 11. Relative orders of magnitude and alternators. 12. Rate of change of a polynomial and approximations of roots. 13. Product polynomials and higher alternators. 14. Degree of approximation to a root. 15. Comparison of polynomials near a root. 240 16. Ordering a simple algebraic extension (in 9). 17. Ordering a simple algebraic extension (outside ⁹t).
Β Neumann (Sat,) studied this question.