Ineffably Ramsey cardinal
- Ineffably Ramsey cardinal
In mathematics, an ineffably Ramsey cardinal (named after Frank P. Ramsey and after ineffable cardinals) is a certain kind of large cardinal number.
Formally, a cardinal number κ such that for every function "f": [ κ] < ω → {0, 1} (with [κ] < ω denoting the set of all finite subsets of κ) there is a stationary set "A" that is homogeneous for "f" (i.e.: for every "n", "f" is constant on the "n"-tuples from "A") is called Ramsey.
It is obvious from the definition that an ineffably Ramsey cardinal is both Ramsey and totally ineffable.
See also
* Almost Ramsey cardinal
* Ramsey cardinal
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Ramsey cardinal — In mathematics, a Ramsey cardinal (named after Frank P. Ramsey) is a certain kind of large cardinal number.Formally, a cardinal number kappa; such that for every function f : [ kappa;] < omega; rarr; {0, 1} (with [ kappa;] < omega; denoting the… … Wikipedia
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