Any sequence satisfying can be adjusted so that , so this is indeed a weakened form of .
Any such sequence actually contains a stationary set of such that for each : given any club and any unbounded , construct a sequence, and , from the elements of each, such that the -th member of is greater than the -th member of , which is in turn greater than any earlier member of . Since both sets are unbounded, this construction is possible, and is a subset of still unbounded in . So there is some such that , and since , is also the limit of a subsequence of and therefore an element of .
|Date of creation||2013-03-22 12:53:52|
|Last modified on||2013-03-22 12:53:52|
|Last modified by||Henry (455)|