The proof-theoretic strength of Ramsey's theorem for pairs and two colors.

@article{Patey2016ThePS,
  title={The proof-theoretic strength of Ramsey's theorem for pairs and two colors.},
  author={Ludovic Patey and K. Yokoyama},
  journal={arXiv: Logic},
  year={2016}
}
  • Ludovic Patey, K. Yokoyama
  • Published 2016
  • Mathematics
  • arXiv: Logic
  • Ramsey's theorem for $n$-tuples and $k$-colors ($\mathsf{RT}^n_k$) asserts that every k-coloring of $[\mathbb{N}]^n$ admits an infinite monochromatic subset. We study the proof-theoretic strength of Ramsey's theorem for pairs and two colors, namely, the set of its $\Pi^0_1$ consequences, and show that $\mathsf{RT}^2_2$ is $\Pi^0_3$ conservative over $\mathsf{I}\Sigma^0_1$. This strengthens the proof of Chong, Slaman and Yang that $\mathsf{RT}^2_2$ does not imply $\mathsf{I}\Sigma^0_2$, and… CONTINUE READING
    25 Citations
    Ramsey's theorem for pairs, collection, and proof size
    • 2
    • PDF
    The Strength of Ramsey's Theorem For Pairs over trees: I. Weak König's Lemma
    • 2
    • PDF
    Some upper bounds on ordinal-valued Ramsey numbers for colourings of pairs
    • 4
    • PDF
    The strength of Ramsey's Theorem for Pairs and arbitrarily Many Colors
    • 2
    • PDF
    Combinatorial principles equivalent to weak induction
    • 2
    • PDF
    An inside/outside Ramsey theorem and recursion theory
    • 2
    • PDF
    The reverse mathematics of Ramsey-type theorems
    • 10
    • PDF
    A weak variant of Hindman’s Theorem stronger than Hilbert’s Theorem
    • L. Carlucci
    • Computer Science, Mathematics
    • Arch. Math. Log.
    • 2018
    • 5
    • PDF

    References

    SHOWING 1-10 OF 77 REFERENCES
    On the Ramseyan Factorization Theorem
    • 10
    • PDF
    Notes on the first-order part of Ramsey's theorem for pairs (Proof theory and complexity)
    • 1
    • PDF
    SOMEWHERE OVER THE RAINBOW RAMSEY THEOREM FOR PAIRS
    • 18
    • PDF
    On The Strength of Ramsey's Theorem for Pairs
    • 193
    • Highly Influential
    • PDF
    Ramsey's Theorem for Pairs and Provably Recursive Functions
    • 11
    • PDF
    The reverse mathematics of Ramsey-type theorems
    • 10
    • PDF
    Random reals, the rainbow Ramsey theorem, and arithmetic conservation
    • 12
    • Highly Influential
    • PDF
    Ramsey's Theorem and Recursion Theory
    • C. Jockusch
    • Computer Science, Mathematics
    • J. Symb. Log.
    • 1972
    • 190
    Combinatorial principles weaker than Ramsey's Theorem for pairs
    • 126
    • Highly Influential
    • PDF
    The strength of infinitary Ramseyan principles can be accessed by their densities
    • 17
    • Highly Influential
    • PDF