Improved bounds are established for the closed Ramsey number R^{cl}(ω·n+1, 3) lying between ω^4·(n-2)+1 and ω^5 for n≥3, together with a general result that ω^θ does not arrow to (ω^α,3) in the closed sense when θ < R(α,3).
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On closed Ramsey numbers of small countable ordinals
Improved bounds are established for the closed Ramsey number R^{cl}(ω·n+1, 3) lying between ω^4·(n-2)+1 and ω^5 for n≥3, together with a general result that ω^θ does not arrow to (ω^α,3) in the closed sense when θ < R(α,3).