数据库理论中结果崩溃的Escherofeucht-Fraisse博弈方法
An Ehrenfeucht-Fraisse Game Approach to Collapse Results in Database Theory
摘要：
我们提出了一个新的Escherifeucht-Fraisse游戏方法崩溃的结果在数据库理论，我们表明，在原则上，这种方法足以证明每个自然的通用崩溃的结果。按照这种方法，我们可以处理某些无限的数据库，而以前的方法是失败的。我们证明了Z-可嵌入数据库在任意线性序上下文结构和任意一元谓词上的自然泛型崩溃，以及N-可嵌入数据库在上下文结构（R，<，+，Mon_Q，Groups）上的自然泛型崩溃。这里，N、Z、R分别表示自然数、整数和实数的集合。Groups是（R，+）中包含Z的所有子群的集合，而Mon_Q是N中特定无限子集Q的所有子集的集合。限制公式的复杂性，可用于制定纯粹存在的一阶公式的布尔组合的查询，我们甚至获得崩溃的N-嵌入数据库在任何线性有序的上下文结构与任意谓词。最后，我们开发了N-可表示的数据库的概念，这是一个自然的推广的经典概念的可表示的数据库。我们表明，N-可嵌入数据库的自然通用崩溃结果可以提升到更大的N-可表示数据库类。特别是为了获得（N，<，+，Mon_Q）的折叠结果，我们在存在内置加法关系+的情况下显式地构造复制器的获胜策略。作为副产品，这也导致了Ginsburg和Spanier定理的Escherichfeucht-Fraisse博弈证明，说明FO（<，+）-句子的谱是半线性的。
英文摘要：
We present a new Ehrenfeucht-Fraisse game approach to collapse results in database theory and we show that, in principle, this approach suffices to prove every natural generic collapse result. Following this approach we can deal with certain infinite databases where previous, highly involved methods fail. We prove the natural generic collapse for Z-embeddable databases over any linearly ordered context structure with arbitrary monadic predicates, and for N-embeddable databases over the context structure (R,<,+,Mon_Q,Groups). Here, N, Z, R, denote the sets of natural numbers, integers, and real numbers, respectively. Groups is the collection of all subgroups of (R,+) that contain Z, and Mon_Q is the collection of all subsets of a particular infinite subset Q of N. Restricting the complexity of the formulas that may be used to formulate queries to Boolean combinations of purely existential first-order formulas, we even obtain the collapse for N-embeddable databases over any linearly ordered context structure with arbitrary predicates. Finally, we develop the notion of N-representable databases, which is a natural generalization of the classical notion of finitely representable databases. We show that natural generic collapse results for N-embeddable databases can be lifted to the larger class of N-representable databases. To obtain, in particular, the collapse result for (N,<,+,Mon_Q), we explicitly construct a winning strategy for the duplicator in the presence of the built-in addition relation +. This, as a side product, also leads to an Ehrenfeucht-Fraisse game proof of the theorem of Ginsburg and Spanier, stating that the spectra of FO(<,+)-sentences are semi-linear.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
