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PCF theory
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== Main definitions == If ''A'' is an infinite set of [[regular cardinal]]s, ''D'' is an [[ultrafilter]] on ''A'', then we let <math>\operatorname{cf}\left(\prod A/D\right)</math> denote the cofinality of the ordered set of functions <math>\prod A</math> where the ordering is defined as follows: <math>f<g</math> if <math>\{x\in A:f(x)<g(x)\}\in D</math>. pcf(''A'') is the set of cofinalities that occur if we consider all ultrafilters on ''A'', that is, <div style="text-align: center;"><math>\operatorname{pcf}(A)=\left\{\operatorname{cf}\left(\prod A/D\right):D\,\,\mbox{is an ultrafilter on}\,\,A\right\}.</math></div>
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