Partitions of trees and ACA'
Bernard A. Anderson, Jeffry L. Hirst
TL;DR
This paper establishes an equivalence between a version of Ramsey's theorem for trees with arbitrary exponents and the subsystem ACA' in reverse mathematics, linking combinatorial principles with logical subsystems.
Contribution
It demonstrates the equivalence of a tree-based Ramsey theorem with the subsystem ACA' in reverse mathematics, extending previous results to arbitrary exponents.
Findings
Ramsey's theorem for trees is equivalent to ACA'
The result applies to arbitrary exponents in the theorem
Links combinatorial principles with logical subsystems
Abstract
We show that a version of Ramsey's theorem for trees for arbitrary exponents is equivalent to the subsystem ACA' of reverse mathematics.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Evolutionary Algorithms and Applications · Philosophy and History of Science