Conway names, the simplicity hierarchy and the surreal number tree
Philip Ehrlich · Journal of Logic and Analysis · 2011
Each surreal number has a unique Conway name (or normal form) that is characteristic of its individual properties.The paper answers the following two questions that are naturally suggested by the surreal number system's structure as a lexicographically ordered full binary tree.(i) Given the Conway name of a surreal number, what are the Conway names of its two immediate successors?(ii) Given the Conway names of the members of a chain of surreal numbers of limit length, what is the Conway name of the immediate successor of the chain?2000 Mathematics