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Corrigendum to “Number Systems with Simplicity Hierarchies: A Generalization of Conway's Theory of Surreal Numbers”

An ordered class (A, <) is said to have cofinal (resp. coinitial) character a if a; is the least ordinal < On such that there is a cofinal (resp. coinitial) subclass of (A, <) that is isomorphic to a (resp. *a = the inverse of a). While having no impact on the proofs of the paper's other results, statement (iii) of Theorem 4 of [1, p. 1237] contains a minor error: it fails to mention that "(A, <) has cofinal character On and coinitial character On." Except for obvious additions, the published proof remains the same and the corrected statement of the theorem reads: Theorem 4. For a lexicographically ordered binary tree (A,<,<s) the following are equivalent: (i) (A,<s) is full; (ii) (A, <, <s) is complete; (iii) (A, <) has cofinal character On and coinitial character On, and the intersection of every nested sequence Ia(0 < a < ? G On) of nonempty convex subclasses of (A,<,<s) is nonempty (and, hence, by Theorem 1, contains a simplest member.) Without the addendum, (iii) would merely imply that (A, <) is a convex subclass of a lexicographically ordered full binary tree.