31. Examples include the theory of real closed ordered fields and the theory of dense linear orderings without endpoints. 32. Then, by the axioms defining an ordered field , & omega;, & omega; 2, and 1 are all positive. 33. The first sense of the term is the geometry over a non-Archimedean ordered field , or a subset thereof. 34. A major line of current research is based on discovering expansions of the real ordered field that are o-minimal. 35. Nevertheless, archaeology did become a more ordered field , in contrast to the individual and sporadic efforts that came before. 36. The plaintiffs'theory will be put to the test Sunday in a court-ordered field test at a Texas military base. 37. Generally we say that the real numbers are described by the axioms of an " Archimedean complete ordered field ". 38. More formally, real numbers have the two basic properties of being an ordered field , and having the least upper bound. 39. *PM : Archimedean ordered fields are real, id = 9819 new !-- WP guess : Archimedean ordered fields are real-- Status: 40. The court-ordered field test is expected to play a key role at the trial, which is set to begin in mid-May.
