In set theory, a Rowbottom cardinal, introduced by Frederick Rowbottom, is a certain kind of large cardinal number.

An uncountable cardinal number is said to be -Rowbottom that is quasi-homogeneous is simply Rowbottom if it is -Rowbottom.

Every Ramsey cardinal is Rowbottom, and every Rowbottom cardinal is Jónsson. By a theorem of Kleinberg, the theories ZFC + “there is a Rowbottom cardinal” and ZFC + “there is a Jónsson cardinal” are equiconsistent.

In general, Rowbottom cardinals need not be large cardinals in the usual sense: Rowbottom cardinals could be singular is Rowbottom” is consistent. If it is, it has much higher consistency strength than the existence of a Rowbottom cardinal. The axiom of determinacy is Rowbottom (but contradicts the axiom of choice).

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