Constructive versions of ordinal number classes

Constructive versions of ordinal number classes
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Trans. Amer. Math. Soc. 100 (1961), 325-369

DOI: https://doi.org/10.1090/S0002-9947-1961-0151396-X

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References

J. W. Addison and S. C. Kleene, A note on function quantification, Proc. Amer. Math. Soc. 8 (1957), 1002–1006. MR 91243, DOI 10.1090/S0002-9939-1957-0091243-2
Heinz Bachmann, Transfinite Zahlen, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Heft 1, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1955 (German). MR 0071481
Alonzo Church, The constructive second number class, Bull. Amer. Math. Soc. 44 (1938), no. 4, 224–232. MR 1563715, DOI 10.1090/S0002-9904-1938-06720-1

Formal definitions in the theory of ordinal numbers

Uniqueness ordinals and extended R-systems

Abraham A. Fraenkel, Abstract set theory, Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Co., Amsterdam, 1953. MR 0056660
Kurt Gödel, The Consistency of the Continuum Hypothesis, Annals of Mathematics Studies, No. 3, Princeton University Press, Princeton, N. J., 1940. MR 0002514

On notation for ordinal numbers

S. C. Kleene, Arithmetical predicates and function quantifiers, Trans. Amer. Math. Soc. 79 (1955), 312–340. MR 70594, DOI 10.1090/S0002-9947-1955-0070594-4
S. C. Kleene, Hierarchies of number-theoretic predicates, Bull. Amer. Math. Soc. 61 (1955), 193–213. MR 70593, DOI 10.1090/S0002-9904-1955-09896-3
Stephen Cole Kleene, Introduction to metamathematics, D. Van Nostrand Co., Inc., New York, N. Y., 1952. MR 0051790
S. C. Kleene and Emil L. Post, The upper semi-lattice of degrees of recursive unsolvability, Ann. of Math. (2) 59 (1954), 379–407. MR 61078, DOI 10.2307/1969708

Analytic predicates and extensions of the notion of constructive ordinal

Azriel Lévy, Axiom schemata of strong infinity in axiomatic set theory, Pacific J. Math. 10 (1960), 223–238. MR 124205
Hartley Rogers Jr., Recursive functions over well ordered partial orderings, Proc. Amer. Math. Soc. 10 (1959), 847–853. MR 111685, DOI 10.1090/S0002-9939-1959-0111685-8
Clifford Spector, Recursive well-orderings, J. Symbolic Logic 20 (1955), 151–163. MR 74347, DOI 10.2307/2266902
Oswald Veblen, Continuous increasing functions of finite and transfinite ordinals, Trans. Amer. Math. Soc. 9 (1908), no. 3, 280–292. MR 1500814, DOI 10.1090/S0002-9947-1908-1500814-9

Remarks on constructive ordinals and set theory

Hao Wang, Ordinal numbers and predicative set theory, Z. Math. Logik Grundlagen Math. 5 (1959), 216–239. MR 132697, DOI 10.1002/malq.19590051403