ar X iv : 1 70 8 . 02 14 5 v 1 [ m at h . L O ] 7 A ug 2 01 7 JOINT DIAMONDS AND LAVER DIAMONDS
نویسنده
چکیده
We study the concept of jointness for guessing principles, such as ♦κ and various Laver diamonds. A family of guessing sequences is joint if the elements of any given sequence of targets may be simultaneously guessed by the members of the family. We show that, while equivalent in the case of ♦κ, joint Laver diamonds are nontrivial new objects. We give equiconsistency results for most of the large cardinals under consideration and prove sharp separations between joint Laver diamonds of different lengths in the case of θ-supercompact cardinals.
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