Zermelo's idea (1908a) was pursued by Kuratowski in the 1920s, thereby generalising and systematising work, not just of Zermelo, but of Hessenberg and Hausdorff too, giving a simple set of necessary and sufficient conditions for a subset ordering to represent a linear ordering. He also argues forcefully that it is in fact undesirable for set theory to go beyond this and present a general theory of ordinal numbers: