On the quasi-ordering of Borel linear orders under embeddability
On the quasi-ordering of Borel linear orders under embeddability
复制标题
可嵌入性下Borel线性阶的拟序
DOI：
10.2307/2274645
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发表时间：
1990
影响因子：
0.6
通讯作者：
J. Saint
中科院分区：
文献类型：
--
作者：
A. Louveau;J. Saint
本文部分地回答了Borel线性序类在可嵌入性下是良拟序的问题。我们证明了对于那些可嵌入Rω的Borel序，在字典序下，确实是这种情况。对于可嵌入到R2中的Borel序，我们的证明在ZFC中有效，但是对于可嵌入到某些Rn（n < ω）中的Borel序，它使用了投射决定性，而对于一般情况，它使用了超投射决定性。
Abstract We provide partial answers to the following problem: Is the class of Borel linear orders well-quasi-ordered under embeddability? We show that it is indeed the case for those Borel orders which are embeddable in Rω, with the lexicographic ordering. For Borel orders embeddable in R2, our proof works in ZFC, but it uses projective determinacy for Borel orders embeddable in some Rn, n < ω, and hyperprojective determinacy for the general case.