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Definably complete Baire structures
We consider definably complete Baire expansions of ordered fields: every definable subset of the domain of the structure has a supremum and the domain cannot be written as the union of a definableExpand
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An effective version of Wilkie's theorem of the complement and some effective o-minimality results
TLDR
We prove an effective version of Wilkie's theorem of the complement, so in particular given an expansion of the ordered field R with finitely many C∞ functions, if there are uniform and computable upper bounds on the number of connected components of quantifier free definable sets. Expand
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On the First-Order Theory of Real Exponentiation
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Definably complete and Baire structures and Pfaffian closure
We consider definably complete and Baire expansions of ordered fields: every definable subset of the domain of the structure has a supremum and the domain can not be written as the union of aExpand
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Theorems of the Complement
This is an expository paper on a Theorem of the Complement, due to Wilkie, and its generalisations. Wilkie (Sel Math (NS) 5:397–421, 1999) gave necessary and sufficient conditions for an expansion ofExpand
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Definably complete and Baire structures
We consider definably complete and Baire expansions of ordered fields: every definable subset of the domain of the structure has a supremum and the domain can not be written as the union of aExpand
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Multivariable Newton-Puiseux Theorem for Generalised Quasianalytic Classes
We show how to solve explicitly an equation satisfied by a real function belonging to certain general quasianalytic classes. Examples of the classes under consideration are the collection ofExpand
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Noetherian varieties in definably complete structures
  • Tamara Servi
  • Mathematics, Computer Science
  • Log. Anal.
  • 18 June 2008
TLDR
We prove that the zero-set of a C∞ function belonging to a noetherian differential ring M can be written as a finite union of C ∞ manifolds which are definable by functions from the same ring. Expand
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