Partitions of large Rado graphs

Archive for Mathematical Logic 48 (6):579-606 (2009)

Let κ be a cardinal which is measurable after generically adding ${\beth_{\kappa+\omega}}$ many Cohen subsets to κ and let ${\mathcal G= ( \kappa,E )}$ be the κ-Rado graph. We prove, for 2 ≤ m < ω, that there is a finite value ${r_m^+}$ such that the set [κ] m can be partitioned into classes ${\langle{C_i:i 2 we have ${r_m^+ > r_m}$ where r m is the corresponding number of types for the countable Rado graph
Keywords Mathematics   Algebra   Mathematics, general   Mathematical Logic and Foundations
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DOI 10.1007/s00153-009-0138-2
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Ramsey Theory for Countable Binary Homogeneous Structures.Jean A. Larson - 2005 - Notre Dame Journal of Formal Logic 46 (3):335-352.

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