AI 中文总结
研究可计算函数的最大最终不同（MED）族的质量问题，通过定义MED族质量问题并与Lempp等人定义的比较，借助Greenberg等人的框架，展示Schrittesser构建的有效封闭MED族，得出相关结果。
AI 中文摘要
连续统的基数特征是实数有趣族的基数。一个经过充分研究的例子是自然数集的最大几乎不相交（MAD）族。在研究基数特征的可计算理论类似物方面已经做了大量工作。Lempp、Miller、Nies和Soskova（2023）通过将MAD族的编码视为单个“通用”集来研究编码MAD族的类。这样的类被称为质量问题；可以研究质量问题之间的相对复杂性。在第2节中，我们以质量问题作为基数特征类似物的研究为基础。我们以同样的方式定义可计算函数的最大最终不同（MED）族的质量问题，并将它们与Lempp等人定义的质量问题进行比较。在第3节中，我们综述了Greenberg、Kuyper和Turetsky（2019）的工作，该工作为基数特征及其有效对应物提供了一个抽象框架。我们表明这个框架适用于在质量问题的背景下获得结果。在第4节中，我们展示了Schrittesser（2018）在集合论中构建的一个有效封闭的MED族。我们表明该构建足够有效，以至于所构建族的可计算成员相对于可计算函数是MED。
英文摘要
Cardinal characteristics of the continuum are the cardinalities of interesting families of reals. A well-studied example is that of maximal almost disjoint (MAD) families of sets of natural numbers. Significant work has been done investigating computability-theoretic analogues of cardinal characteristics. By considering encodings of MAD families as a single `universal' set, Lempp, Miller, Nies, and Soskova (2023) studied the class of encoded MAD families. Such a class is referred to as a mass problem; one can study the relative complexity between mass problems. In Section 2, we build on the study of mass problems as analogues of cardinal characteristics. We define mass problems of maximal eventually different (MED) families of computable functions in the same way and compare them against the mass problems defined by Lempp et al. In Section 3, we survey work by Greenberg, Kuyper, and Turetsky (2019) that provides an abstract framework for cardinal characteristics and their effective counterparts. We show that this framework is suitable for obtaining results in the setting of mass problems. In Section 4, we showcase a construction by Schrittesser (2018) of an effectively closed MED family in set theory. We show that the construction is sufficiently effective that the computable members of the constructed family are MED relative to computable functions.
