大基数指的是其存在性能够推出ZF系统协调性的基数。如不可达基数、Ramsay基数、紧致性基数和可测基数等，其中可测基数和Ramsay基数都比弱紧基数强，而若假定AC，弱紧基数是不可达基数。

In the mathematical field of set theory, a large cardinal property is a certain kind of property of transfinite cardinal numbers. Cardinals with such properties are, as the name suggests, generally very "large" (for example, bigger than the least α such that α=ω_α). The proposition that such cardinals exist cannot be proved in the most common axiomatization of set theory, namely ZFC, and such propositions can be viewed as ways of measuring how "much", beyond ZFC, one needs to assume to be able to prove certain desired results. In other words, they can be seen, in Dana Scott's phrase, as quantifying the fact "that if you want more you have to assume more".