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Ordered exponential fields
Preliminaries on valued and ordered modules Non-archimedean exponential fields Valuation theoretic interpretation of the growth and Taylor axioms The exponential rank Construction of exponentialExpand
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Positivity, sums of squares and the multi-dimensional moment problem
Let K be the basic closed semi-algebraic set in R n defined by some finite set of polynomials S and T, the preordering generated by S. For K compact, f a polynomial in n variables nonnegative on KExpand
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Embedding ordered fields in formal power series fields
In the paper it is shown how an embedding of an ordered field F into a formal power series field can be extended canonically to an embedding of any simple extension F(y) of F. Properties of theExpand
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Ax-Kochen-Ershov principles for valued and ordered vector spaces
We study extensions of valued vector spaces with variable base field, introducing the notion of disjointness and valuation disjointness in this setting. We apply the results to determine the modelExpand
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Sums of squares and moment problems in equivariant situations
We begin a systematic study of positivity and moment problems in an equivariant setting. Given a reductive group G over R acting on an affine R-variety V, we consider the induced dual action on theExpand
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On the structure of nonarchimedean exponential fields I
  • S. Kuhlmann
  • Mathematics, Computer Science
  • Arch. Math. Log.
  • 1 June 1995
TLDR
We compute the natural valuation and skeleton of the ordered multiplicative group (K>0, ·, 1, <) in terms of those of theordered additive groups (K,+,0,<). Expand
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Isomorphisms of lexicographic powers of the reals
Given a chain F, we consider the lexicographic order llr. If A is a chain such that Rr IRA, we examine the question of whether necessarily F A. Under an additional hypothesis, we show that F and AExpand
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On ηα-groups and fields
Let κ:=ℵα. The following are known: two ηα-sets of power κ are isomorphic. Let α>0. Two ordered divisible Abelian groups that are ηα-sets of power κ are isomorphic, two real closed fields that areExpand
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Hardy type derivations on generalised series fields
Abstract We consider the valued field K : = R ( ( Γ ) ) of generalised series (with real coefficients and monomials in a totally ordered multiplicative group Γ). We investigate how to endow K with aExpand
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Hardy type derivations on fields of exponential logarithmic series
Abstract We consider the valued field K : = R ( ( Γ ) ) of formal series (with real coefficients and monomials in a totally ordered multiplicative group Γ). We investigate how to endow K with aExpand
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