In set theory, a Rowbottom cardinal, introduced by Rowbottom (1971), is a certain kind of large cardinal number.
-Rowbottom if for every function f: [κ]<ω → λ (where λ < κ) there is a set H of order type
that is quasi-homogeneous for f, i.e., for every n, the f-image of the set of n-element subsets of H has <
By a theorem of Kleinberg, the theories ZFC + “there is a Rowbottom cardinal” and ZFC + “there is a Jónsson cardinal” are equiconsistent.
If it is, it has much higher consistency strength than the existence of a Rowbottom cardinal.
is Rowbottom (but contradicts the axiom of choice).
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