Quantification of number-theoretic functions

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1. J.W. Addison and S.C. Kleene [1] A note on function quantification, Proc. Amer. Math. Soc., vol. 8 (1957), pp. 1002—1006. Zbl0084.24901
2. A. Church [2] Introduction to mathematical logic, vol. 1, Princeton, N. J. (Princeton Univ. Press), 1956, x + 376 pp. Zbl0073.24301MR82931
3. A. Church and S.C. Kleene [3] Formal definitions in the theory of ordinal numbers, Fund. Math., vol. 28 (1936), pp. 11—21. In the definition of ×O on p. 18, the case b is 0O should have been treated separately (so a X O 0O conv 0O). Zbl0016.00201JFM63.0029.02
4. S.C. Kleene [4] Introduction to metamathematics, Amsterdam (North Holland), Groningen (Noordhoff), New York and Toronto (Van Nostrand), 1952, X + 550 pp. Zbl0047.00703MR51790
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6. [6] On the forms of the predicates in the theory of constructive ordinals (second paper), vol. 77 (1955), pp. 405—428. Zbl0067.25203
7. [7] Hierarchies of number-theoretic predicates, Bull. Amer. Math. Soc., vol. 61 (1955), pp. 193—213. Zbl0066.25901
8. S.C. Kleene and E.L. Post [8] The upper semi-lattice of degrees of recursive unsolvability, Ann. of Math. (2), vol. 59 (1954), pp. 379—407. Zbl0057.24703
9. C. Spector [9] Recursive well-orderings, Jour. Symbolic Logic, vol. 20 (1955), pp. 151-163. Zbl0067.00303MR74347

1. G. Kreisel, La prédicativité
2. Philippe de Rouilhan, Towards finishing off the axiom of reducibility