WEAK COMPARABILITY OF WELL ORDERINGS AND REVERSE MATHEMATICS

被引：23

作者：

FRIEDMAN, HM

HIRST, JL

机构：

[1] Department of Mathematics, The Ohio State University, Columbus, OH 43210-1174

来源：

ANNALS OF PURE AND APPLIED LOGIC | 1990年 / 47卷 / 01期

关键词：

D O I：

10.1016/0168-0072(90)90014-S

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Two countable well orderings are weakly comparable if there is an order preserving injection of one into the other. We say the well orderings are strongly comparable if the injection is an isomorphism between one ordering and an initial segment of the other. In [5], Friedman announced that the statement "any two countable well orderings are strongly comparable" is equivalent to ATR0. Simpson provides a detailed proof of this result in Chapter 5 of [13]. More recently, Friedman has proved that the statement "any two countable well orderings are weakly comparable" is equivalent to ATR0. The main goal of this paper is to give a detailed exposition of this result. © 1990.

引用

页码：11 / 29

页数：19

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