Document type
ArticleVersion
Published versionPublication date
Publication license
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/228931
Reflecting measures
Journal Title
Authors
Director/Tutor
Additional contribution
Journal ISSN
Volume Title
Abstract
We give new, purely combinatorial characterizations of several kinds of large cardinals, such as strongly $C^{(n)}$-compact and $C^{(n)}$-extendible, in terms of reflecting measures. We then study the key property of tightness of elementary embeddings that witness strong $C^{(n)}$-compactness, which prompts the introduction of the new large-cardinal notion of tightly $C^{(n)}$-compact cardinal. Then we prove, assuming the Ultrapower Axiom, that a cardinal is tightly $C^{(n)}$-compact if and only if it is either $C^{(n-1)}$-extendible or a measurable limit of $C^{(n-1)}$-extendible cardinals. In the last section we also give new characterizations of $\Sigma_n$-strong cardinals in terms of reflecting extenders.
Related resource
Subject
Subject (English)
Citation
Citation
BAGARIA, Joan and GOLDBERG, Gabriel. Reflecting measures. Advances in Mathematics. 2024. Vol. 443. ISSN 0001-8708. [consulted: 16 of October of 2026]. Available at: https://hdl.handle.net/2445/228931