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Partition properties are perhaps the most fruitful of the various methods for defining and discussing large cardinals in set theory. In this paper we weaken in a natural way the most well known of these partition properties and examine the extent to which the cardinals defined remain "large."doi:10.1090/s0002-9939-1971-0281626-7 fatcat:rgavodpzznew3ipqu5wusobbee