A generalization of Rado's theorem on independent transversals
Hazel Perfect · Mathematical Proceedings of the Cambridge Philosophical Society · 1969
The growth of transversal theory has been greatly enriched by the study of abstract independence. In this development, Rado's theorem on independent transversals (4) has played a prominent role, and recent work (e.g. by Welsh(7)) suggests that its applications are by no means exhausted. Rado's theorem can be extended in many directions, and my object is to describe a further generalization (Theorem 2 below) which does not seem to have been noted in the literature.