Good projective witnesses

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2025-05-05 DOI:10.1016/j.apal.2025.103606

Vera Fischer , Sy David Friedman , David Schrittesser , Asger Törnquist

引用次数: 0

Abstract

We develop a new forcing notion for adjoining self-coding cofinitary permutations and use it to show that consistently, the minimal cardinality

a_{g}

of a maximal cofinitary group (MCG) is strictly between

ℵ_{1}

and

c

, and there is a

Π_{2}^{1}

-definable MCG of this cardinality. Here

Π_{2}^{1}

is optimal, making this result a natural counterpart to the Borel MCG of Horowitz and Shelah. Our theorem has its analogue in the realm of maximal almost disjoint (MAD) families, extending a line of results regarding the definability properties of MAD families in models with large continuum.

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好的投影证人

本文提出了相邻自编码共限置换的一个新的强制概念，并利用它证明了最大共限群（MCG）的最小基数ag严格地存在于λ 1和λ c之间，并且存在这个基数的Π21-definable MCG。这里Π21是最优的，使这个结果与霍洛维茨和希拉的Borel MCG自然对应。我们的定理在极大几乎不相交族（MAD）领域有类似的结果，扩展了关于大连续统模型中极大几乎不相交族的可定义性的一系列结果。

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.