Tall, Strong, and Strongly Compact Cardinals
DOI:
https://doi.org/10.5644/SJM.15.01.02Keywords:
Supercompact cardinal, strongly compact cardinal, strong cardinal, tall cardinal, non-reflecting stationary set of ordinals, indestructibilityAbstract
We construct three models in which there are different relationships among the classes of strongly compact, strong, and non-strong tall cardinals. In the first two of these models, the strongly compact and strong cardinals coincide precisely, and every strongly compact/strong cardinal is a limit of non-strong tall cardinals. In the remaining model, the strongly compact cardinals are precisely characterized as the measurable limits of strong cardinals, and every strongly compact cardinal is a limit of non-strong tall cardinals. These results extend and generalize those of of [3] and [1].
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