Editing PCF theory (section)

== Unsolved problems ==
The most notorious conjecture in pcf theory states that |pcf(''A'')|=|''A''| holds for every set ''A'' of regular cardinals with |''A''|<min(''A''). This would imply that if ℵ<sub>ω</sub> is strong limit, then the sharp bound
<div style="text-align: center;"><math>2^{\aleph_\omega}<\aleph_{\omega_1}</math></div>
holds. The analogous bound
<div style="text-align: center;"><math>2^{\aleph_{\omega_1}}<\aleph_{\omega_2}</math></div>
follows from [[Chang's conjecture]] ([[Menachem Magidor|Magidor]]) or even from the nonexistence of a [[Kurepa tree]] ([[Saharon Shelah|Shelah]]).

A weaker, still unsolved conjecture states that if |''A''|<min(''A''), then pcf(''A'') has no inaccessible limit point. This is equivalent to the statement that pcf(pcf(''A''))=pcf(''A'').