
TL;DR
This paper revisits the concept of Super Black Boxes in set theory, focusing on cases where the coloring functions are continuous, and proves their existence for various regular cardinals, with implications for Abelian groups.
Contribution
It extends the theory of Super Black Boxes to continuous colorings and establishes their existence for all regular cardinals, including the critical cases of leph_0 and leph_1.
Findings
Super Black Boxes exist for all regular leph_ and leph_ under continuous coloring assumptions.
The paper proves the existence of multiple ar C-s and free subsets of f^.
Results have implications for the structure of Abelian groups.
Abstract
Let be cardinals, with and regular. Concentrating on a simple case, we say that the triple has a Super Black Box when the following holds. For some stationary and , where is a club of of order type , for every coloring with , there exists such that for every , for stationarily many , we have . In an earlier work, it was proved (along with much more) that for a class of cardinals this holds for many pairs .…
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Taxonomy
TopicsAdvanced Topology and Set Theory · Rings, Modules, and Algebras · Fuzzy and Soft Set Theory
