Club stationary reflection and other combinatorial principles at ℵω+2

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2024-07-01 DOI:10.1016/j.apal.2024.103489

引用次数: 0

Abstract

In this paper we continue the study in [11] of compactness and incompactness principles at double successors, focusing here on the case of double successors of singulars of countable cofinality. We obtain models which satisfy the tree property and club stationary reflection at these double successors. Moreover, we can additionally obtain either approachability or its failure. We also show how to obtain our results on $ℵ_{ω + 2}$ by incorporating collapses; particularly relevant for these circumstances is a new indestructibility theorem of ours showing that posets satisfying certain linked assumptions preserve club stationary reflection.

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ℵω+2处的俱乐部静止反射和其他组合原理

在本文中，我们将继续研究双继点的紧凑性和不紧凑性原则，重点是可数同频奇点的双继点。我们得到了在这些双继点上满足树性质和俱乐部静止反映的模型。此外，我们还能得到可接近性或其失败。我们还展示了如何通过结合坍缩来获得我们的结果；与这些情况特别相关的是我们的一个新的不灭性定理，它表明满足某些关联假设的正集保留了俱乐部静止反映。

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.