Cantor流形的有效强迫
Effective forcing with Cantor manifolds
摘要：
一个整数集合$A$称为全，如果有一个算法，给定一个$A$的枚举，枚举$A$的补数，如果有一个算法，给定一个$A$的补数的枚举，枚举$A$，称为共。在可计算性理论中研究了总体性和总体性的许多变体。本文通过强无穷维Cantor流形的有效强迫构造，将Zapletal的“half-Cohen”强迫有效化（即，的强迫），我们构造了一个整数集合，其计数度是余全的，几乎全的，但既不是圆柱余全的，也不是telograph余全的。
英文摘要：
A set $A$ of integers is called total if there is an algorithm which, given an enumeration of $A$, enumerates the complement of $A$, and called cototal if there is an algorithm which, given an enumeration of the complement of $A$, enumerates $A$. Many variants of totality and cototality have been studied in computability theory. In this note, by an effective forcing construction with strongly infinite dimensional Cantor manifolds, which can be viewed as an effectivization of Zapletal's "half-Cohen" forcing (i.e., the forcing with Henderson compacta), we construct a set of integers whose enumeration degree is cototal, almost total, but neither cylinder-cototal nor telograph-cototal.
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。
