关于可列结构的DPRM性质的注记
Notes on the DPRM property for listable structures
摘要：
这是M. Davis，H. Putnam，J. Robinson，and Y. Matiyasevich表明，一组整数是listable当且仅当它是积极的存在可定义的算术语言。我们调查类似的结构赋予了一个listable介绍这一结果。当这种类似物成立时，该结构被称为具有DPRM性质。我们证明了几个结果解决这个问题的基础方面，如唯一性的listable介绍，转移的DPRM属性下的解释，其关系与积极存在的双解释。我们的研究结果的第一个应用程序是严格的证明（强版本）的几个民俗事实转让的DPRM财产。我们发展的理论的另一个应用是，它将允许我们将各种丢番图与DPRM性质是否适用于全局场的问题联系起来。这最后一个主题包括研究定义丢番图集所需的存在量词的数量。
英文摘要：
A celebrated result by M. Davis, H. Putnam, J. Robinson, and Y. Matiyasevich shows that a set of integers is listable if and only if it is positive existentially definable in the language of arithmetic. We investigate analogues of this result over structures endowed with a listable presentation. When such an analogue holds, the structure is said to have the DPRM property. We prove several results addressing foundational aspects around this problem, such as uniqueness of the listable presentation, transference of the DPRM property under interpretation, and its relation with positive existential bi-interpretability. A first application of our results is the rigorous proof of (strong versions of) several folklore facts regarding transference of the DPRM property. Another application of the theory we develop is that it will allow us to link various Diophantine conjectures to the question of whether the DPRM property holds for global fields. This last topic includes a study of the number of existential quantifiers needed to define a Diophantine set.
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