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THE COLORING OF THE TREE OF COLORINGS
Keywords:
tree in set theory, additive colorings.DOI:
https://doi.org/10.17654/0974165822050Abstract
In the present paper, we continue the investigation of a relation between trees and colorings that was introduced in [1].
In [1], two mappings were defined: a function $C \mapsto T(C)$ assigns to each coloring a tree, and a function $(T, e) \mapsto C(T, e)$ assigns to each tree with an enumeration a coloring. Here we show that the coloring $C$ is not reconstructable from $T(C)$, although the tree $T$ is reconstructable from $C(T, e)$, under certain restrictions on $T$ and $e$.
Received: October 1, 2022
Accepted: November 4, 2022
References
Adi Jarden and Shami Ziv, A note on edge colorings and trees, Mathematical Logic Quarterly 167 (2022), 447-457.
Assaf Rinot, Chain conditions of products, and weakly compact cardinals, Bull. Symbolic Logic 20(3) (2014), 293-314.
Saharon Shelah, The monadic theory of order, Annals of Mathematics 102(3) (1975), 379-419.
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