解析阶关系的线性化
Linearization of analytic order relations
摘要：
我们证明了如果$\leq$是一个解析偏序，那么任何一个$\leq$都可以扩展为一个（黑体）$Δ^1_2$线性序类似于$2^{<ω_1}$中的反链字典序或嵌入$\leq.$中的某个Borel偏序$\leq_0$给出了解析等价关系的一些推论，例如，如果$E$是$Σ^1_1[z]$等价关系，使得$E_0$不嵌入到$E$中，则通过与在$L[z]$中编码E-不变量Borel集的交集来确定$E$。
英文摘要：
We prove that if $\leq$ is an analytic partial order then either $\leq$ can be extended to a (boldface) $Δ^1_2$ linear order similar to an antichain in $2^{<ω_1}$ ordered lexicographically or a certain Borel partial order $\leq_0$ embeds in $\leq.$ Some corollaries for analytic equivalence relations are given, for instance, if $E$ is a $Σ^1_1[z]$ equivalence relation such that $E_0$ does not embed in $E$ then $E$ is determined by intersections with E-invariand Borel sets coded in $L[z]$.
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