Remarks on partition ordinals
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After a brief survey of the theory of partition ordinals, i.e., ordinals α such that α → (α,n)2 for all n < ω, it is shown that MA(ℵ1) implies that ω1ω and ω1ω2 are partition ordinals. This contrasts with an old result of Erdős and Hajnal that α ↛ (α,3)2 holds for both these ordinals under the Continuum Hypothesis.
KeywordsOrder Type Dartmouth College Doubling Property Complete Subgraph Hereditary Property
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