A Partition Theorem of $omega^{omega^{alpha}}$

Notre Dame Journal of Formal Logic 59 (3):387-403 (2018)
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Abstract

We consider finite partitions of the closure F¯ of an ωα-uniform barrier F. For each partition, we get a homogeneous set having both the same combinatorial and topological structure as F¯, seen as a subspace of the Cantor space 2N.

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