A good lightface Δn1 well-ordering of the reals does not imply the existence of boldface Δn−11 well-orderings

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2024-02-28 DOI:10.1016/j.apal.2024.103426

Vladimir Kanovei, Vassily Lyubetsky

引用次数: 0

Abstract

We make use of a finite support product of the Jensen-type forcing notions to define a model of the set theory $ZFC$ in which, for a given $n \geq 3$ , there exists a good lightface $Δ_{n}^{1}$ well-ordering of the reals but there are no any (not necessarily good) well-orderings in the boldface class $Δ_{n - 1}^{1}$ .

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良好的光面 Δn1 有序排列并不意味着存在黑体 Δn-11 有序排列

我们利用詹森类型强制概念的有限支持乘积定义了一个集合论模型，在这个模型中，对于给定的，存在一个良好的光面有序实数，但在黑体类中不存在任何（不一定是良好的）有序实数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of Pure and Applied Logic 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

200 days

期刊介绍： The journal Annals of Pure and Applied Logic publishes high quality papers in all areas of mathematical logic as well as applications of logic in mathematics, in theoretical computer science and in other related disciplines. All submissions to the journal should be mathematically correct, well written (preferably in English)and contain relevant new results that are of significant interest to a substantial number of logicians. The journal also considers submissions that are somewhat too long to be published by other journals while being too short to form a separate memoir provided that they are of particular outstanding quality and broad interest. In addition, Annals of Pure and Applied Logic occasionally publishes special issues of selected papers from well-chosen conferences in pure and applied logic.