Unreachability of Γ2n+1,m

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2025-04-23 DOI:10.1016/j.apal.2025.103604

Derek Levinson

引用次数: 0

Abstract

We find bounds for the maximal length of a sequence of distinct

Γ_{2n + 1, m}

-sets under AD and show there is no sequence of distinct

Γ_{2n + 1}

-sets of length

δ_{2n + 3}^{1}

. As a special case, there is no sequence of distinct

Γ_{1, m}

-sets of length

ℵ_{m + 2}

. These are the optimal results for the pointclasses

Γ_{2n + 1}

and

Γ_{1, m}

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无法到达Γ2n+1，m

我们找到了在AD条件下具有不同Γ2n+1，m-集的序列的最大长度的界，并证明不存在具有不同Γ2n+1-集的序列，其长度为δ2n+31。作为一种特殊情况，不存在不同的序列Γ1，m-长度为λ m+2的集合。这些是pointclass Γ2n+1和Γ1，m的最佳结果。

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.