The combinatorial essence of supercompactness
Christoph Wei{\ss}
TL;DR
This paper introduces combinatorial principles that characterize supercompactness and strong compactness for various cardinals, providing new insights into their consistency and lower bounds.
Contribution
It presents novel combinatorial principles that characterize supercompactness and strong compactness, extending their applicability to successor cardinals and establishing optimal consistency results.
Findings
Characterization of strong compactness and supercompactness via combinatorial principles
Establishment of consistency from optimal assumptions
Application of weak square failure to derive lower bounds
Abstract
We introduce combinatorial principles that characterize strong compactness and supercompactness for inaccessible cardinals but also make sense for successor cardinals. Their consistency is established from what is supposedly optimal. Utilizing the failure of a weak version of square, we show that the best currently known lower bounds for the consistency strength of these principles can be applied.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Mathematical and Theoretical Analysis