论文标题
分离原理为给定有效的投影sigma级的模型
A model in which the Separation principle holds for a given effective projective Sigma-class
论文作者
论文摘要
在本文中，我们证明了以下内容：如果$ n \ ge3 $，则有$ l $的通用扩展 - 可构造的宇宙 - 确实，分离原理对于有效的（Lightface）类$ \ varsigma^1_n $和$ \ \ \ varpi^1_n $用于集合整体的整体。结果是在很久以前由Leo Harrington宣布的，其素描以$ n = 3 $宣布；它的全部证据从未得到过介绍。我们的方法是基于几乎划分的迫使概念独立于Jensen-Solovay的可数产物。
In this paper, we prove the following: If $n\ge3$, there is a generic extension of $L$ -- the constructible universe -- in which it is true that the Separation principle holds for both effective (lightface) classes $\varSigma^1_n$ and $\varPi^1_n$ for sets of integers. The result was announced long ago by Leo Harrington with a sketch of the proof for $n=3$; its full proof has never been presented. Our methods are based on a countable product of almost-disjoint forcing notions independent in the sense of Jensen--Solovay.
