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Journal of Symbolic Logic
Article . 2019 . Peer-reviewed
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JOINT DIAMONDS AND LAVER DIAMONDS

Joint diamonds and Laver diamonds
Authors: Miha E. Habic;

JOINT DIAMONDS AND LAVER DIAMONDS

Abstract

Abstract The concept of jointness for guessing principles, specifically ${\diamondsuit _\kappa }$ and various Laver diamonds, is introduced. 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. While equivalent in the case of ${\diamondsuit _\kappa }$ , 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.

Related Organizations
Keywords

joint Laver functions, Large cardinals, FOS: Mathematics, 03E55, 03E35, Consistency and independence results, Mathematics - Logic, Logic (math.LO), Other combinatorial set theory, Laver functions, joint diamond sequences

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
Green
bronze