驯服的对数指数超级数微分域对
Tame pairs of transseries fields
AI总结：
研究对数指数超级数微分域理论的驯服模型对，包括其完备性、模型完备性、量词消去等性质，以及较小模型和常数域的稳定嵌入性，还推广到微分 - 亨赛尔 - 刘维尔闭预 - $H$ - 域并建立相关结果。
摘要：
本文关注对数指数超级数微分域理论的模型对，其作为实闭域对是驯服的，即较小模型在较大模型内有界且存在标准部分映射。这涵盖了超级数、超现实数的微分域或配备适当超级数微分域扩张的最大哈代域等。该对理论在自然语言中是完备且模型完备的，在通过两个谓词和标准部分映射扩展的同一语言中有量词消去。此外，较小模型在该对中是纯稳定嵌入的，常数域也是。更一般地，研究了微分 - 亨赛尔 - 刘维尔闭预 - $H$ - 域，并在相对于微分剩余域的设定下建立了类似结果。
英文摘要：
This paper concerns pairs of models of the theory of the differential field of logarithmic-exponential transseries that are tame as a pair of real closed fields. That is, the smaller model is bounded inside the larger model and there exists a standard part map. This covers for instance the differential fields of hyperseries or surreal numbers or maximal Hardy fields equipped with suitable enlargements of the differential field of transseries. The theory of such pairs is complete and model complete in a natural language and it has quantifier elimination in the same language expanded by two predicates and a standard part map. Additionally, the smaller model is purely stably embedded in the pair, and hence so is the constant field. More generally, we study differential-Hensel-Liouville closed pre-$H$-fields, i.e., pre-$H$-fields that are differential-henselian, real closed, and closed under exponential integration, equipped with lifts of their differential residue fields, and establish similar results in that setting relative to the differential residue field.
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