Turing computations on ordinals

被引：42

作者：

Koepke, P ^{[1
]}

机构：

[1] Univ Bonn, Math Inst, D-53115 Bonn, Germany

来源：

BULLETIN OF SYMBOLIC LOGIC | 2005年 / 11卷 / 03期

关键词：

D O I：

10.2178/bsl/1122038993

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We define the notion of ordinal computability by generalizing standard TURING computability on tapes of length omega to computations on tapes of arbitrary ordinal length. We show that a set of ordinals is ordinal computable from a finite set of ordinal parameters if and only if it is an element of GODEL'S constructible universe L. This characterization can be used to prove the generalized continuum hypothesis in L.

引用

页码：377 / 397

页数：21