On ordered division rings

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).