当所有集合都是普遍贝尔时，确定性的一致性强度

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics Pub Date : 2025-09-24 DOI:10.1016/j.aim.2025.110548

Sandra Müller

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引用次数: 0

摘要

众所周知，决定性公理的强大的基本力量，如果加上所有实数集合都是普遍的假设，就比决定性公理本身强大得多。Sargsyan推测它就像一个枢机的存在一样强大，这个枢机既是伍丁枢机的极限，也是强枢机的极限。Larson， Sargsyan和Wilson对Woodin的模型构造进行了推广，以证明这种推测的结果是最优的。本文介绍了一种新的杂交小鼠翻译程序，用于扩展Steel， Zhu和Sargsyan的工作，并应用它来证明Sargsyan猜想。

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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The consistency strength of determinacy when all sets are universally Baire

It is known that the large cardinal strength of the Axiom of Determinacy when enhanced with the hypothesis that all sets of reals are universally Baire is much stronger than the Axiom of Determinacy itself. Sargsyan conjectured it to be as strong as the existence of a cardinal that is both a limit of Woodin cardinals and a limit of strong cardinals. Larson, Sargsyan and Wilson used a generalization of Woodin's derived model construction to show that this conjectured result would be optimal. In this paper we introduce a new translation procedure for hybrid mice extending work of Steel, Zhu and Sargsyan and apply it to prove Sargsyan's conjecture.

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来源期刊

Advances in Mathematics 数学-数学

CiteScore

2.80

自引率

5.90%

发文量

497

审稿时长

7.5 months

期刊介绍： Emphasizing contributions that represent significant advances in all areas of pure mathematics, Advances in Mathematics provides research mathematicians with an effective medium for communicating important recent developments in their areas of specialization to colleagues and to scientists in related disciplines.