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Can the strong tree property hold simultaneously at every successor of a singular cardinal across an arbitrary class of such cardinals without any large cardinal upper bound stronger than a supercompact?

Related: Mitchell's theorem on the tree property at omega two, Magidor-Shelah theorem on successors of singular cardinals, Unger's results on the tree property along many cardinals

The strong tree property and its sibling the super tree property are combinatorial principles that generalize the tree property, and researchers have been working to force these principles to hold at successors of singular cardinals, particularly along long sequences or segments of such cardinals. The known consistency results require large cardinal hypotheses of varying strength, and a central unresolved question is whether one can achieve the strong tree property at the successor of every singular cardinal in some broad class simultaneously, and if so exactly what large cardinal strength is necessary and sufficient to do so. The gap between what is known for individual cardinals or finite segments versus an unbounded class of successors of singulars remains wide open.

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