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Ultraproducts and Chevalley groups
TLDR
We prove the decidability of the set of sentences true in almost all finite groups of the form L(K) where K is a finite field and L a fixed untwisted Chevalley type. Expand
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Topological differential fields
TLDR
We consider first-order theories of topological fields admitting a model-completion and their expansion to differential fields (requiring no interaction between the derivation and the other primitives of the language). Expand
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Essentially periodic ordered groups
TLDR
A totally ordered group G is essentially periodic if for every deniable non-trivial convex subgroup H of G every denable subset of G is equal to a nite union of cosets of subgroups of G on some interval containing an end segment of H . Expand
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On decidable extensions of Presburger arithmetic: from A. Bertrand numeration sytems to Pisot numbers
  • Françoise Point
  • Computer Science, Mathematics
  • Journal of Symbolic Logic
  • 1 September 2000
TLDR
We study extensions of Presburger arithmetic with a unary predicate R and we show that under certain conditions on R, R is sparse (a notion introduced by A. L. Semënov) and the theory of 〈ℕ, +, R〉 is decidable. Expand
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Free abelian lattice-ordered groups
TLDR
We prove that the theory of the free abelian lattice-ordered group on n generators is undecidable if n > 2. Expand
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dans les corps ordonnés différentiellement clos On differentially closed ordered fields
We prove that the theory CODF of ordered differentially closed fields is definably complete and uniformly finite. We deduce that the open core of any model of CODF is o-minimal using a recent resultExpand
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Groups of Polynomial Growth and Their Associated Metric Spaces
Let YN be the space associated with a finitely generated group G and a nonstandard natural number N. We prove the following two results. If YN is locally compact and has finite Minkowski dimension,Expand
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The valuation difference rank of a quasi-ordered difference field
There are several equivalent characterizations of the valuation rank of an ordered or valued field. In this paper, we extend the theory to the case of an ordered or valued {\it difference} fieldExpand
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