FORCING WITH BUSHY TREES

被引：4

作者：

Khan, Mushfeq ^{[1
]}

Miller, Joseph S. ^{[2
]}

机构：

[1] Univ Hawaii Manoa, Dept Math, Honolulu, HI 96822 USA

[2] Univ Wisconsin, Dept Math, Madison, WI 53706 USA

来源：

BULLETIN OF SYMBOLIC LOGIC | 2017年 / 23卷 / 02期

关键词：

Diagonally noncomputable functions; bushy tree forcing; minimal degrees; algorithmic randomness; DIAGONALLY NONRECURSIVE FUNCTIONS;

D O I：

10.1017/bsl.2017.12

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present several results that rely on arguments involving the combinatorics of "bushy trees". These include the fact that there are arbitrarily slow-growing diagonally noncomputable (DNC) functions that compute no Kurtz random real, as well as an extension of a result of Kumabe in which we establish that there are DNC functions relative to arbitrary oracles that are of minimal Turing degree. Along the way, we survey some of the existing instances of bushy tree arguments in the literature.

引用

页码：160 / 180

页数：21

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