Short definitions of the ordinals
Kenneth R. Brown, Hao Henry Wang · Journal of Symbolic Logic · 1966
In this paper, a simple inductive characterization of the ordinal numbers is stated and developed. The characterization forms the basis for a set of axioms for ordinal theory and also for several short explicit definitions of the ordinals. The axioms are shown to be sufficient for ordinal theory, and, subject to suitable existence assumptions, each of the definitions is shown to imply the axioms. The present results apply to the familiar von Neumann version of the ordinals, but the methods used are easily adapted to other versions.