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If r ≥ 0 is finite and κ is an infinite cardinal, then + (+) + where exp 0 (κ) = κ and inductively exp r+1 (κ)=2 exp r (κ).This is sharp in the sense that exp r (κ) + cannot be replaced by exp r (κ) on the left hand side.
Paul Erdős, Chao Ko, and Richard Rado proved this theorem in 1938 after working together on it in England. Rado had moved from Berlin to the University of Cambridge and Erdős from Hungary to the University of Manchester, both escaping the influence of Nazi Germany; Ko was a student of Louis J. Mordell at Manchester. [6]