可接近的自由子集和精细结构衍生尺度

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2024-03-16 DOI:10.1016/j.apal.2024.103428

Dominik Adolf, Omer Ben-Neria

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引用次数: 0

摘要

谢拉证明，内部可接近子代数上自由子集的存在是由正则红心数间隔的 PCF 猜想的失败引起的。我们证明了一个更强的性质，即 "可接近有界子集性质"（Approachable Bounded Subset Property）。此外，我们还研究了连续树状尺度的相关概念，并证明这种尺度一定存在于典型内部模型的所有乘积上。我们利用这一结果，再加上一个覆盖类型的论证，来证明强制部分的大底假设是最优的。

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Approachable free subsets and fine structure derived scales

Shelah showed that the existence of free subsets over internally approachable subalgebras follows from the failure of the PCF conjecture on intervals of regular cardinals. We show that a stronger property called the Approachable Bounded Subset Property can be forced from the assumption of a cardinal λ for which the set of Mitchell orders ${o (μ) | μ < λ}$ is unbounded in λ. Furthermore, we study the related notion of continuous tree-like scales, and show that such scales must exist on all products in canonical inner models. We use this result, together with a covering-type argument, to show that the large cardinal hypothesis from the forcing part is optimal.

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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.