** 4. Strongly compact cardinals and **

Definition 1A cardinal isstrongly compactiff it is uncountable, and any -complete filter (over any set ) can be extended to a -complete ultrafilter over

The notion of strong compactness has its origin in infinitary logic, and was formulated by Tarski as a natural generalization of the compactness of first order logic. Many distinct characterizations have been found.

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