Milner–Rado paradox

In set theory, a branch of mathematics, the Milner – Rado paradox, found by Eric Charles Milner and Richard Rado (1965), states that every ordinal number α less than the successor κ⁺ of some cardinal number κ can be written as the union of sets X₁,X₂,... where X_n is of order type at most κⁿ for n a positive integer.

References

• Milner, E. C.; Rado, R. (1965), "The pigeon-hole principle for ordinal numbers", Proc. London Math. Soc. (3) 15: 750–768, doi:10.1112/plms/s3-15.1.750, MR0190003