产生共解析集的超穷归纳法
Transfinite inductions producing coanalytic sets
摘要：
A. Miller证明了协分析两点集、Hamel基和MAD族的相容存在性。在这些情况下，经典的超穷归纳法可以被修改以产生一个协解析集。我们推广了他的结果，并给出了一个条件，使之能很容易地应用于这类情况。作为一个新的应用，我们证明了在$V=L$中存在一个与可数集上的所有$C^1$曲线相交的平面的不可数余解析子集.
英文摘要：
A. Miller proved the consistent existence of a coanalytic two-point set, Hamel basis and MAD family. In these cases the classical transfinite induction can be modified to produce a coanalytic set. We generalize his result formulating a condition which can be easily applied in such situations. We reprove the classical results and as a new application we show that in $V=L$ there exists an uncountable coanalytic subset of the plane that intersects every $C^1$ curve in a countable set.
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。
