Necessary and sufficient conditions for the existence of a n - subtle cardinal
نویسنده
چکیده
We extend the work of Abe in [?], to show that the strong partition relation C → (n+ 2) <−reg, for every C ∈ WNS ∗ κ,λ, is a consequence of the existence of an n-subtle cardinal. We then build on Kanamori’s result in [?], that the existence of an n-subtle cardinal is equivalent to the existence of a set of ordinals containing a homogeneous subset of size n + 2 for each regressive coloring of n+1-tuples from the set. We use this result to show that a seemingly weaker relation, in the context of Pκλ is also equivalent. This relation is a new type of regressive partition relation, which we then attempt to characterize.
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