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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Uniform properties of rigid subanalytic sets
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by Leonard Lipshitz and Zachary Robinson PDF
Trans. Amer. Math. Soc. 357 (2005), 4349-4377 Request permission


In the context of rigid analytic spaces over a non-Archimedean valued field, a rigid subanalytic set is a Boolean combination of images of rigid analytic maps. We give an analytic quantifier elimination theorem for (complete) algebraically closed valued fields that is independent of the field; in particular, the analytic quantifier elimination is independent of the valued field’s characteristic, residue field and value group, in close analogy to the algebraic case. This provides uniformity results about rigid subanalytic sets. We obtain uniform versions of smooth stratification for subanalytic sets and the Łojasiewicz inequalities, as well as a unfiorm description of the closure of a rigid semianalytic set.
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Additional Information
  • Leonard Lipshitz
  • Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
  • Email:
  • Zachary Robinson
  • Affiliation: Department of Mathematics, East Carolina University, Greenville, North Carolina 27858
  • Email:
  • Received by editor(s): March 7, 2003
  • Published electronically: June 21, 2005
  • Additional Notes: This work was supported in part by NSF grant number DMS 0070724
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 357 (2005), 4349-4377
  • MSC (2000): Primary 03C10, 32P05, 32B20; Secondary 26E30, 03C98
  • DOI:
  • MathSciNet review: 2156714