is a combinatoric principle weaker than . It states that, for stationary in , there is a sequence such that and and with the property that for each unbounded subset there is some .
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 .