Description: Define the successor of a class. When applied to an ordinal number, the
successor means the same thing as "plus 1" (see oa1suc ). Definition
7.22 of TakeutiZaring p. 41, who use "+ 1" to denote this function.
Ordinal natural numbers defined using this successor function and 0 as the
empty set are also called von Neumann ordinals; 0 is the empty set {}, 1
is {0, {0}}, 2 is {1, {1}}, and so on. Our definition is a generalization
to classes. Although it is not conventional to use it with proper
classes, it has no effect on a proper class ( sucprc ), so that the
successor of any ordinal class is still an ordinal class ( ordsuc ),
simplifying certain proofs. Some authors denote the successor operation
with a prime (apostrophe-like) symbol, such as Definition 6 of Suppes
p. 134 and the definition of successor in Mendelson p. 246 (who uses the
symbol "Suc" as a predicate to mean "is a successor ordinal"). The
definition of successor of Enderton p. 68 denotes the operation with a
plus-sign superscript. (Contributed by NM, 30-Aug-1993)