发表机构
The Czech Academy of Sciences（捷克科学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文用逻辑和拓扑空间的紧致性刻画了多种Berkeley型大基数，表明紧致性假设可违反选择公理和V=HOD，从而提升已知一致性强度。
AI 中文摘要
我们通过逻辑的紧致性性质，并等价地通过某些拓扑空间的紧致性性质，刻画了exacting、rank-Berkeley、Berkeley以及club Berkeley基数。这将已知可由紧致性陈述获得的强度提升到无选择大基数公理的领域，这些公理在一致性强度方面是已知最强的陈述。此外，它表明紧致性假设可以直接违反选择公理和公理$V=\ ext{HOD}$。
英文摘要
We characterise exacting, rank-Berkeley, Berkeley, and club Berkeley cardinals by compactness properties of logics and, equivalently, by compactness properties of certain topological spaces. This raises the strength known to be obtainable by statements about compactness into the realm of choiceless large cardinal axioms, the strongest known statements in terms of consistency strength. Moreover, it shows that compactness assumptions can directly violate the axiom of choice and the axiom $V=\text{HOD}$.
Comments23 pages; added explicit statement of one result from the literature for improved self-containedness
