Topic
Supercompact cardinal
About: Supercompact cardinal is a research topic. Over the lifetime, 240 publications have been published within this topic receiving 3388 citations.
Papers published on a yearly basis
Papers
TL;DR: In this article, it was proved that strongly compact cardinals are consistent and it is consistent to assume that the first such cardinal is the first measurable cardinal, and that the existence of supercompact cardinals is also consistent.
143 citations
TL;DR: In this article, it was proved that the existence of supercompact cardinal is equivalent to a certain Skolem-Lowenheim Theorem for second order logic, whereas the presence of extendible cardinal is also equivalent to compactness theorem for that logic.
Abstract: It is proved that the existence of supercompact cardinal is equivalent to a certain Skolem-Lowenheim Theorem for second order logic, whereas the existence of extendible cardinal is equivalent to a certain compactness theorem for that logic. It is also proved that a certain axiom schema related to model theory implies the existence of many extendible cardinals.
117 citations
TL;DR: The lottery preparation works best when performed after fast function forcing, which adds a new completely general kind of Laver function for any large cardinal, thereby freeing the Laer function concept from the supercompact cardinal context.
117 citations
TL;DR: It is shown that if the HOD Conjecture is true then this provides strong evidence for the existence of an ultimate version of Godel's constructible universe L.
Abstract: We investigate both iteration hypotheses and extender models at the level of one supercompact cardinal. The HOD Conjecture is introduced and shown to be a key conjecture both for the Inner Model Program and for understanding the limits of the large cardinal hierarchy. We show that if the HOD Conjecture is true then this provides strong evidence for the existence of an ultimate version of Godel's constructible universe L. Whether or not this "ultimate" L exists is now arguably the central issue for the Inner Model Program.
91 citations
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TL;DR: In this article, it was shown that there are no ℵn-Aronszajn trees for any finiten⩾2, starting from a model with infinitely many supercompact cardinals.
80 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 6 |
| 2020 | 6 |
| 2019 | 7 |
| 2018 | 9 |
| 2017 | 15 |
| 2016 | 13 |