不使用句子的斯科特-卡普分析
Scott-Karp analysis without sentences
AI总结：
本文提出了一种不依赖无穷级语言的抽象斯科特-卡普分析，用于研究拓扑群作用下的全局相似性等价关系。
摘要：
斯科特和卡普给出了一个分析，该分析在两个结构之间的全局相似性和局部共同性之间提供了逐层等价性。斯科特和卡普的局部不变量是某些无穷级语言公式。我们给出了斯科特-卡普分析局部方面的更抽象版本，避免使用无穷级语言。我们显示所得到的层级结构在经典设置中仍然提供期望的等价性。此外，我们证明了分析的抽象性质使其适合在拓扑群作用于拓扑群的背景下提供局部逐层等价于霍杰特的更一般版本的全局相似性。我们进一步提供了类似于埃亨费乌特和弗拉伊塞经典工作的新的博弈论等价关系，用于霍杰特的全局相似性关系和一些自然变体。
英文摘要：
Scott and Karp gave an analysis which provides a level-by-level equivalence between global similarity between two structures and local commonality in terms of sharing particular invariants. Scott and Karp's local invariants were certain infinitary formulae. We give a more abstract version of the local side of Scott-Karp analysis which avoids the use of infinitary languages. We show the resulting hierarchies are still provide desired equivalences in the classical setting. Moreover, the abstract nature of our analysis, as we show, makes it suitable to provide local level-by-level equivalents to Hjorth's much more general version of global similarity in the context of topological group actions on topological groups. We, furthermore, provide, analogously to the classical work of Ehrenfeucht and Fraïssé, novel game theoretic equivalents for Hjorth's global similarity relations and some natural variants.
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。
