Closed asymptotic couples
Closed asymptotic couples
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闭合渐近偶
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
L. Dries
中科院分区：
文献类型：
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作者：
Matthias Aschenbrenner;L. Dries
Hardy域的求导在其值群上推导出一个函数Ψ。如果Hardy域扩展实域并在幂下封闭，则其值群也是一个向量空间。这样的“含有Ψ-function的有序向量空间”被称为h对。我们定义了闭h对，并证明了每个h对都可以嵌入到一个闭h对中。关键的事实是，闭h偶有一个消去理论：任意方程组和不等式（由向量空间操作、函数Ψ、参数和待解的未知数建立）的可解性等价于系统参数的有效条件。极大Hardy域的h -对是闭的，对数列域的h -对也是闭的。我们详细地分析了给定h对的有限生成扩展。
The derivation of a Hardy field induces on its value group a certain function Ψ If a Hardy field extends the real field and is closed under powers, then its value group is also a vector space over ℝ. Such “ordered vector spaces with Ψ-function” are called H-couples. We define closed H-couples and show that every H-couple can be embedded into a closed one. The key fact is that closed H-couples have an elimination theory: solvability of an arbitrary system of equations and inequalities (built up from vector space operations, the function Ψ, parameters, and the unknowns to be solved for) is equivalent to an effective condition on the parameters of the system. The H-couple of a maximal Hardy field is closed, and this is also the case for the H-couple of the field of logarithmic-exponential series over ℝ. We analyze in detail finitely generated extensions of a given H-couple.