Ramsey's theorem for singletons and strong computable reducibility

  title={Ramsey's theorem for singletons and strong computable reducibility},
  author={Damir D. Dzhafarov and Ludovic Patey and R. Solomon and L. Westrick},
  journal={arXiv: Logic},
  • Damir D. Dzhafarov, Ludovic Patey, +1 author L. Westrick
  • Published 2016
  • Mathematics
  • arXiv: Logic
  • We answer a question posed by Hirschfeldt and Jockusch by showing that whenever $k > \ell$, Ramsey's theorem for singletons and $k$-colorings, $\mathsf{RT}^1_k$, is not strongly computably reducible to the stable Ramsey's theorem for $\ell$-colorings, $\mathsf{SRT}^2_\ell$. Our proof actually establishes the following considerably stronger fact: given $k > \ell$, there is a coloring $c : \omega \to k$ such that for every stable coloring $d : [\omega]^2 \to \ell$ (computable from $c$ or not… CONTINUE READING
    14 Citations


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