Transversals for ordinal intervals (Q1095907)

If I is a closed interval [\(\alpha\),\(\beta\) ] of ordinals, the length \(\lambda\) (I) of I is defined to be \(\beta -\alpha +1\). The authors prove the following theorem, which was conjectured by A. P. Huhn: If S is a set of closed intervals of ordinals such that any two different intervals of them have different lengths, then S has a transversal \((=\) an injective choice function).