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Quite complete real closed fields

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Abstract

We prove that any ordered field can be extended to one for which every decreasing sequence of bounded closed intervals, of any length, has a nonempty intersection; equivalently, there are no Dedekind cuts with equal cofinality from both sides.

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References

  1. D. Scott,On complete ordered fields, inApplications of Model Theory to Algebra, Analysis, and Probability (W. A. J. Luxemburg, ed.), Holt, Rinehart, and Winston, New York, 1969, pp. 274–278.

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Authors and Affiliations

  1. Institute of Mathematics, The Hebrew University of Jerusalem, Givat Ram, 91904, Jerusalem, Israel

    Saharon Shelah

  2. Department of Mathematics, Rutgers University, 08854, New Brunswick, NJ, USA

    Saharon Shelah

Authors
  1. Saharon Shelah
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Correspondence to Saharon Shelah.

Additional information

Research supported by the United States-Israel Binational Science Foundation. Publication 757.

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Shelah, S. Quite complete real closed fields. Isr. J. Math. 142, 261–272 (2004). https://doi.org/10.1007/BF02771536

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  • DOI: https://doi.org/10.1007/BF02771536

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