Tall, Strong, and Strongly Compact Cardinals

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].