The Jensen Covering Property

An optimal extension of the Jensen covering lemma, within the limits imposed by Prikry forcing, is proved. If L[E] is an "iterable" weasel with no measurable cardinals, then either L[E] has "indiscernibles", or every uncountable set of ordinals is contained in a set in L[E] of the same cardinality. (The terms "iterable" and "indiscernibles" are made precise in the paper.) Most importantly, there is no hypothesis explicitly limiting the large cardinals which are consistent in L[E].

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