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Results tagged with ramsey-theory
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user 4600
Branch of combinatorics with the philosophy that 'total disorder is impossible'. For example, Ramsey's theorem asserts that for each $n$, every sufficiently large graph either contains a clique of size $n$ or a stable set of size $n$.
9
votes
Accepted
Is Van der Waerden's function elementary
Yes, this should follow from the elementary bound. The point is that having a Kalmar elementary time bound is "closed under" searches through exponentially large collections.
Suppose $N=W(r,k)$ is lea …
- 24.8k
18
votes
Why is this new result such a big deal?
They show that $\DeclareMathOperator{\WKL}{WKL}\DeclareMathOperator{\RT}{RT}\DeclareMathOperator{\RCA}{RCA} \RT^2_2$ is $\Pi^0_3$-conservative over $\RCA_0$. Thus, there is no way that $\RT^2_2$ can b …
- 24.8k