Mathematical Logic Quarterly 55 (2):201-211 (2009)

Abstract
We prove that for each β, γ < ε0 there existsα < ε0 such that whenever A ⊆ ω is α -large and G: A → β is such that ) ≤ a), then there exists a γ -large C ⊆ A on which G is nondecreasing. Moreover, we give upper bounds for α for small ordinals β ≤ ωmath image
Keywords Hardy hierarchy  α ‐large sets
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DOI 10.1002/malq.200710089
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