关于Needed Reals
On needed reals
摘要：
在布拉斯之后，我们称实数a为实数上的二元关系R的“needed”，如果在每个R-适当集合中我们找到一个元素，从中a是图灵可计算的。我们证明了Cof（N）所需的每个实数都是超算术。用“具有最小基数的R-adequate”代替“R-adequate”，我们得到了“弱需要”的相关概念。我们证明了这两个概念对于收割关系是不一致的。(They在许多模型中是一致的）。我们表明，并不是所有的超算术实数需要的收割关系。这回答了布拉斯在1999年12月的Oberwolfach会议上提出的一些问题。
英文摘要：
Following Blass, we call a real a ``needed'' for a binary relation R on the reals if in every R-adequate set we find an element from which a is Turing computable. We show that every real needed for Cof(N) is hyperarithmetic. Replacing ``R-adequate'' by ``R-adequate with minimal cardinality'' we get related notion of being ``weakly needed''. We show that is is consistent that the two notions do not coincide for the reaping relation. (They coincide in many models.) We show that not all hyperarithmetical reals are needed for the reaping relation. This answers some questions asked by Blass at the Oberwolfach conference in December 1999.
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