论文标题
关于可列出结构的DPRM属性的注释
Notes on the DPRM property for listable structures
论文作者
论文摘要
M. Davis，H。Putnam，J。Robinson和Y. Matiyasevich的著名结果表明，当且仅当它在算术的语言中是积极定义的时，一组整数是可以列出的。我们研究了该结果的类似物，而不是具有可列出的陈述的结构。当这样的模拟成立时，据说该结构具有DPRM财产。我们证明了几个涉及有关此问题的基本方面的结果，例如可列出的呈现的唯一性，解释中的DPRM属性的转移以及其与积极存在的双重纠正性的关系。我们结果的第一个应用是（强大版本的）关于DPRM属性转移的几个民俗事实的严格证明。我们开发的理论的另一个应用是，它将允许我们将各种二芬太丁的猜想与DPRM属性是否具有全球领域的问题联系起来。最后一个主题包括对定义毒液剂组所需的存在量化符数量的研究。
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.
