关于模糊集和函数的计算性质
On the computational properties of ambivalent sets and functions
AI总结：
本文研究了模糊函数和集合的计算性质，探讨了Δ类上各种操作的计算等价性，并提出了决定模糊集合非空性的结构函数。
摘要：
不连续函数的例子早在欧拉、阿贝尔、狄利克雷、傅里叶和布尔扎诺的工作中就已经出现。巴依尔的一项突破性发现是许多不连续函数在某种程度上是良好的，即它们是连续函数序列的点wise极限；后者现在被称为“巴依尔1类”。我们将研究一个严格位于半连续和巴依尔1类之间的函数类，称为模糊函数。特别是，我们研究模糊函数和集合的计算性质，记作Δ，使用克里尔的S1-S9方案。在Δ上各种标准操作（ supremum，巴依尔1表示，……）的计算等价性被建立，包括决定给定模糊集合是否非空的结构函数Ω_Δ。一个选择器被证明可以相对于Ω_Δ和克里尔的量词∃²计算。
英文摘要：
Examples of discontinuous functions already appear in the work of Euler, Abel, Dirichlet, Fourier, and Bolzano. A ground-breaking discovery due to Baire was that many discontinuous functions are well-behaved in that they are the pointwise limit of a sequence of continuous functions; the latter form a class nowadays simply called `Baire 1'. We shall study a class strictly between the semi-continuous and Baire 1 functions, called the ambivalent fuctions. In particular, we investigate the computational properties of the class of ambivalent functions and sets, denoted $\bf Δ$, working with Kleene's S1-S9 schemes. Computational equivalences for various standard operations (supremum, Baire 1 representation, \dots) on $\bf Δ$ are established, including the structure functional $Ω_{\bf Δ}$ that decides if a given ambivalent set is non-empty. A selector is shown to be computable relative to $Ω_{\bf Δ}$ and Kleene's quantifier $\exists^{2}$.
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。
