Conway names, the simplicity hierarchy and the surreal number tree | Zendy

Philip Ehrlich | Zendy

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Conway names, the simplicity hierarchy and the surreal number tree

Author(s) -

Philip Ehrlich

Publication year - 2011

Publication title -

journal of logic and analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.278

H-Index - 4

ISSN - 1759-9008

DOI - 10.4115/jla.2011.3.1

Subject(s) - mathematics , successor cardinal , hierarchy , combinatorics , lexicographical order , binary tree , tree (set theory) , chain (unit) , limit (mathematics) , discrete mathematics , law , mathematical analysis , physics , astronomy , political science

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?

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