Corpus ID: 85465466

# Effectiveness for the Dual Ramsey Theorem

@article{Dzhafarov2017EffectivenessFT,
title={Effectiveness for the Dual Ramsey Theorem},
author={Damir D. Dzhafarov and S. Flood and R. Solomon and L. Westrick},
journal={arXiv: Logic},
year={2017}
}
• Damir D. Dzhafarov, +1 author L. Westrick
• Published 2017
• Mathematics
• arXiv: Logic
• We analyze the Dual Ramsey Theorem for $k$ partitions and $\ell$ colors ($\mathsf{DRT}^k_\ell$) in the context of reverse math, effective analysis, and strong reductions. Over $\mathsf{RCA}_0$, the Dual Ramsey Theorem stated for Baire colorings is equivalent to the statement for clopen colorings and to a purely combinatorial theorem $\mathsf{cDRT}^k_\ell$. When the theorem is stated for Borel colorings and $k\geq 3$, the resulting principles are essentially relativizations of \$\mathsf{cDRT}^k_… CONTINUE READING
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