Editing Upper and lower bounds (section)

==Exact upper bounds==
An upper bound {{mvar|u}} of a subset {{mvar|S}} of a preordered set {{math|(''K'', ≤)}} is said to be an ''exact upper bound'' for {{mvar|S}} if every element of {{mvar|K}} that is strictly majorized by {{mvar|u}} is also majorized by some element of {{mvar|S}}. Exact upper bounds of [[reduced product|reduced products]] of [[linear order|linear orders]] play an important role in [[PCF theory]].<ref>{{Cite journal|url=https://www.sciencedirect.com/science/article/pii/S0168007298000116|title=Exact upper bounds and their uses in set theory|last=Kojman|first=Menachem|journal=Annals of Pure and Applied Logic |date=21 August 1998 |volume=92 |issue=3 |pages=267–282 |doi=10.1016/S0168-0072(98)00011-6 }}</ref>