Hierarchies of effective descriptive set theory
HTML articles powered by AMS MathViewer
- by Peter G. Hinman PDF
- Trans. Amer. Math. Soc. 142 (1969), 111-140 Request permission
References
-
J. W. Addison, On some points of the theory of recursive functions, Ph.D. dissertation, Univ. of Wisconsin, Madison, 1954.
—, Analogies in the Borel, Lusin, and Kleene hierarchies. I and II, Abstracts 139 and 341, Bull. Amer. Math. Soc. 61 (1955), 75, 171-172.
- J. W. Addison, Separation principles in the hierarchies of classical and effective descriptive set theory, Fund. Math. 46 (1959), 123–135. MR 131357, DOI 10.4064/fm-46-2-123-135
- Logic, methodology and philosophy of science, Stanford University Press, Stanford, Calif., 1962. MR 0166069
- J. W. Addison, Some problems in hierarchy theory, Proc. Sympos. Pure Math., Vol. V, American Mathematical Society, Providence, R.I., 1962, pp. 123–130. MR 0141599
- J. W. Addison, The method of alternating chains, Theory of Models (Proc. 1963 Internat. Sympos. Berkeley), North-Holland, Amsterdam, 1965, pp. 1–16. MR 0201313
- 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 R. F. Barnes, The classification of the closed-open and the recursive sets of number-theoretic functions, Ph.D. dissertation, Univ. of California, Berkeley, 1965. G. M. Benson, The theory of definability in applied predicate languages for number theory, Ph.D. dissertation, Univ. of California, Berkeley, 1966. E. Borel, Le calcul des intégrales définis, J. Math. Pures Appl. 8 (1912), 159-210. R. O. Gandy, General recursive functionals of finite type and hierarchies of functions, mimeographed copy of a paper given at the symposium on Mathematical Logic held at the University of Clermont-Ferrand, June, 1962. Similar material will appear in the Proceedings of the Summer School in Mathematical Logic held at the University of Leicester, August, 1964.
- Felix Hausdorff, Set theory, 2nd ed., Chelsea Publishing Co., New York, 1962. Translated from the German by John R. Aumann et al. MR 0141601 P. G. Hinman, Ad astra per aspera: hierarchy schemata in recursive function theory, Ph.D. dissertation, Univ. of California, Berkeley, 1966. L. Kantorovitch and E. Livenson, Memoir on the analytical operations and projective sets. I and II, Fund. Math. 18 (1932), 214-279; 20 (1933), 54-97.
- Stephen Cole Kleene, Introduction to metamathematics, D. Van Nostrand Co., Inc., New York, N. Y., 1952. MR 0051790
- 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
- S. C. Kleene, Recursive functionals and quantifiers of finite types. I, Trans. Amer. Math. Soc. 91 (1959), 1–52. MR 102480, DOI 10.1090/S0002-9947-1959-0102480-9
- Stephen Cole Kleene and Richard Eugene Vesley, The foundations of intuitionistic mathematics, especially in relation to recursive functions, North-Holland Publishing Co., Amsterdam, 1965. MR 0176922 A. N. Kolmogorov, Operations on sets, Mat. Sb. 35 (1928), 414-422. (Russian) K. Kunugui, Sur un théorème d’existence dans la théorie des ensembles projectifs, Fund. Math. 29 (1937), 167-181. K. Kuratowski, Topologie, 4th ed., Vol. 1, PWN, Warsaw, 1958, xii + 494 pp. H. Lebesgue, Sur les fonctions representables analytiquement, J. Math. Pures Appl. (6) 1 (1905), 139-216. A. A. Ljapunov, R-sets, Trudy Mat. Inst. Steklov. 40 (1953). (Russian)
- A. A. Lyapunov, On the classification of $R$-sets, Mat. Sbornik N.S. 32(74) (1953), 255–262 (Russian). MR 0064103 N. N. Luzin, Leçons sur les ensembles analytiques, Gauthier-Villars, Paris, 1930, xvi + 238 pp.
- Yiannis N. Moschovakis, Hyperanalytic predicates, Trans. Amer. Math. Soc. 129 (1967), 249–282. MR 236010, DOI 10.1090/S0002-9947-1967-0236010-2
- Yiannis N. Moschovakis, Abstract first order computability. I, II, Trans. Amer. Math. Soc. 138 (1969), 427–464. MR 244045, DOI 10.1090/S0002-9947-1969-0244045-0 G. E. Sacks, Degrees of unsolvability, Ann. of Math. Studies No. 55, Princeton Univ. Press, Princeton, N. J., 1963, xi + 174 pp. E. Selivanovskij, On a class of effective sets (sets C), Mat. Sb. 35 (1928), 379-413. M. Suslin, Sur une définition des ensembles mesurables B sans nombres transfinis, C. R. Acad. Sci. Paris 164 (1917), 88-91.
Additional Information
- © Copyright 1969 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 142 (1969), 111-140
- MSC: Primary 02.77
- DOI: https://doi.org/10.1090/S0002-9947-1969-0265161-3
- MathSciNet review: 0265161