Transactions of the American Mathematical Society · 1961 · 10 citations · 12 references
2) Note that we are using integers (set theoretic objects) rather than numerals (syntactical objects) as labels. Although the use of numerals would be closer to our motivation, the use of integers simplifies statements of theorems and proofs. For our purposes the distinction is of minor importance.
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On notation for ordinal numbers
S. C. Kleene · Journal of Symbolic Logic · 1938 · 755 citations
Clifford Spector · Journal of Symbolic Logic · 1955 · 209 citations
Hierarchies of number-theoretic predicates
S. C. Kleene · Bulletin of the American Mathematical Society · 1955 · 184 citations · Full text