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