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, S. Flood, +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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