An uncountable cardinal is strongly compact when every -satisfiable theory in any language is satisfiable, with no bound on the number of nonlogical symbols.

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Strongly compact cardinal by Wikipedia Bot 1
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A strongly compact cardinal is a certain kind of large cardinal in set theory, which is a branch of mathematical logic. Large cardinals are certain kinds of infinite cardinal numbers that have strong properties and are much larger than the standard infinite cardinals (like countable and uncountable cardinals).
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