适当扩充n-REA集
Extending Properly n-REA Sets
摘要：
Soare和Stob在[5]中证明了：如果$A$是一个r. e.不可计算的集合，那么有一个形式为$A \oplus W^A_e$的集合，它不是r.e.图灵度如果我们定义一个真$n+1$ -REA集为一个与任何$n$ -REA集都不是图灵等价的$n+1$ -REA集，这个结果表明每一个真1-REA集都可以扩展为一个真2-REA集. Cholak和Hinman在[1]中推广了这个结果，证明了每个2-REA集都可以推广到一个适当的3-REA集。这自然导致了这样的假设：每个正确的$n$ -REA集合都可以扩展为正确的$n+1$ -REA集合.在本文中，我们证明了这个假设是错误的，存在一个正常的$3$ -REA集，它不能扩展到一个正常的$4$ -REA集。
英文摘要：
In [5] Soare and Stob prove that if $A$ is an r.e. set which isn't computable then there is a set of the form $A \oplus W^A_e$ which isn't of r.e. Turing degree. If we define a properly $n+1$-REA set to be an $n+1$-REA set which isn't Turing equivalent to any $n$-REA set this result shows that every properly 1-REA set can be extended to a properly 2-REA set. This result was extended in [1] by Cholak and Hinman who proved that every 2-REA set can be extended to a properly 3-REA set. This leads naturally to the hypothesis that every properly $n$-REA set can be extended to a properly $n+1$-REA set. In this paper, we show this hypothesis is false and that there is a properly $3$-REA set which can't be extended to a properly $4$-REA 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。
