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Recursion-Theoretic Hierarchies

Book description

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. The theory set out in this volume, the ninth publication in the Perspectives in Logic series, is the result of the meeting and common development of two currents of mathematical research: descriptive set theory and recursion theory. Both are concerned with notions of definability and with the classification of mathematical objects according to their complexity. These are the common themes which run through the topics discussed here. The author develops a general theory from which the results of both areas can be derived, making these common threads clear.

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References
Aanderaa, S. 1974 Inductive definitions and their closure ordinals, in Fenstad-Hinman [1974], 207-220.
Ackermann, W. 1928 Zum Hilbertschen Aufbau der reelen Zahlen, Math. Annalen 99 (1928) 118-133.
Aczel, P. 1970 Representability in some systems of second order arithmetic, Israel Jour. Math. (1970) 309-328.
Aczel, P. 1975 Quantifiers, games, and inductive definitions, in Kanger [1975], 1-14.
Aczel, P. and Hinman, P.G. 1974 Recursion in the superjump, in Fenstad-Hinman [1974], 3-41.
Aczel, P. and Richter, W.H. 1974 Inductive definitions and reflecting properties of admissible ordinals, in Fenstad-Hinman [1974], 301-381.
Addison, J.W. Jr. 1954 On Some Points of the Theory of Recursive Functions, Ph.D. thesis; University of Wisconsin, Madison, 1954, 92 pp.
Addison, J.W. Jr. 1955 Analogies in the Borel, Lusin, and Kleene hierarchies, I, II (abstracts), Bull. Amer. Math. Soc. 61 (1955) 75, 171-172.
Addison, J.W. Jr. 1959 Separation principles in the hierarchies of classical and effective descriptive set theory, Fund. Math. 46 (1959) 123-135.
Addison, J.W. Jr. 1959a Some consequences of the axiom of constructibility, Fund. Math. 46 (1959) 337-357.
Addison, J.W. Jr. 1965 The undefinability of the definable (abstract), Notices Amer. Math. Soc. 12 (1965) 347.
Addison, J.W. Jr. and Moschovakis, Y.N. 1968 Some consequences of the axiom of definable determinateness, Proc. Nat. Acad. Sci. USA 59 (1968) 708-712.
Amstislavskij, V.I. 1970 Effective R-sets and transfinite extensions of recursive hierarchies, Fund. Math. 68 (1970) 61-68.
Amstislavskij, V.I. 1970a On the decomposition of a field of sets obtained by an R -operation over recursive sets, Soviet Mathematics 11 (1970) 419-422.
Anonymous, 1961 Infinitistic Methods (Proceedings of the Symposium on Foundations of Mathematics, Warsaw, 1959), Pergamon Press, Oxford, 1961, 362 pp.
Bar-Hillel, Y. 1965 Logic, Methodology, and Philosophy of Science II (Proceedings of the International Congress, Jerusalem, 1964, Editor), North-Holland, Amsterdam, 1965, 440 pp.
Bar-Hillel, Y. 1970 Mathematical Logic and Foundations of Set Theory (Proceedings of an international colloquium, Jerusalem, 1968, Editor), North-Holland, Amsterdam, 1970, 145 pp.
Bar-Hillel, Y., Poznanski, E.I.J., Rabin, M.O., and Robinson, A. 1961 Essays on the Foundations of Mathematics (Dedicated to A.A. Fraenkel on his seventieth anniversary, Editors), Magnus Press, Hebrew University, Jerusalem, 1961, 351 pp.
Barnes, R.F. 1965 The classification of recursive sets of number-theoretic functions (abstract), Notices Amer. Math. Soc. 12 (1965) 622-623.
Barwise, K.J. 1975 Admissible Sets and Structures, Perspectives in Mathematical Logic 1, Springer-Verlag, Berlin-Heidelberg-New York, 1975, 394 pp.
Barwise, K.J. 1977 Handbook of Mathematical Logic, North-Holland, Amsterdam, 1977.
Barwise, K.J. and Fisher, E. 1970 The Shoenfield absoluteness lemma, Israel Jour. Math. 8 (1970) 329-339.
Blackwell, D. 1967 Infinite games and analytic sets, Proc. Nat. Acad. Sci. U.S.A. 58 (1967) 1836-1837.
Bulloff, J.J., Hahn, S.W., and Holyoke, T.C. 1969 Foundations of Mathematics (Symposium papers commemorating the sixtieth birthday of Kurt Gödel, Columbus, Ohio, 1966, Editors), Springer-Verlag, Berlin-Heidelberg-New York, 1969, 195 pp.
Cenzer, D. 1974 Ordinal recursion and inductive definitions, in Fenstad-Hinman [1974], 221-264.
Cenzer, D. 1974a Analytic inductive definitions, Jour. Symb. Log. 39 (1974) 310-312.
Cenzer, D. 1974b Inductively defined sets of reals, Bull. Amer. Math. Soc. 80 (1974) 485-487.
Chang, C.C. and Moschovakis, Y.N. 1970 The Suslin-Kleene theorem for Vκ with cofinality (κ)= ω, Pacific Jour. Math. 35 (1970) 565-569.
Clarke, D.A. 1964 Hierarchies of Predicates of Finite Types, Memoirs of the Amer. Math. Soc. 51, American Mathematical Society, Providence, R.I., 1964, 95 pp.
Cohen, P.J. 1963/64 The independence of the continuum hypothesis, I, II, Proc. Nat. Acad. Sci. U.S.A. 50 (1963) 1143-1148, 51 (1964) 105-110.
Crossley, J.N. 1967 Sets, Models, and Recursion Theory (Proceedings of the Summer School in Mathematical Logic and Logic Colloquium, Leicester, England, 1965, Editor), North-Holland, Amsterdam, 1967, 331 pp.
Davis, M. 1964 Infinite games of perfect information, Advances in Game Theory, Annals of Math. Studies 52 (1964) 85-101.
Dekker, J.C.E. 1962 Recursive Function Theory (Proceedings of the Fifth Symposium in Pure Mathematics of the Amer. Math. Soc, New York, 1961, Editor), American Mathematical Society, Providence, R.I., 1962, 247 pp.
Devlin, K.J. 1973 Aspects of Constructibility, Lecture Notes in Mathematics 354, Springer-Verlag, Berlin-Heidelberg-New York, 1973, 240 pp.
Devlin, K.J. 1974 An introduction to the fine structure of the constructible hierarchy (results of Ronald Jensen), in Fenstad-Hinman [1974], 123-163.
Enderton, H.B. 1964 Hierarchies in recursive function theory, Trans. Amer. Math. Soc. 1ll (1964) 457-471.
Enderton, H.B. 1970 The unique existential quantifier, Archiv. f. math. Logik und Grundl. 13/1-2 (1970) 52-54.
Enderton, H.B. 1972 A Mathematical Introduction to Logic, Academic Press, New York, 1972, 293 pp.
Feferman, S. 1964/65 Some applications of the notions of forcing and generic sets, Fund. Math. 56 (1964/65) 325-345.
Fenstad, J.E. 1971 Proceedings of the Second Scandanavian Logic Symposium (Oslo, 1970, Editor), North- Holland, Amsterdam, 1971, 413 pp.
Fenstad, J.E. 1971a The axiom of determinateness, in Fenstad [1971], 41-61.
Fenstad, J.E. 1974 On axiomatizing recursion theory, in Fenstad-Hinman [1974], 385-404.
Fenstad, J.E. 1975 Computation theories: an axiomatic approach to recursion on general structures, in Müller et al. [1975], 143-168.
Fenstad, J.E. 1980? Computation Theories: an Axiomatic Approach to Recursion on General Structures, Perspectives in Mathematical Logic, Springer-Verlag, Berlin-Heidelberg-New York, to appear.
Fenstad, J.E. and Hinman, P.G. 1974 Generalized Recursion Theory (Proceedings of the 1972 Oslo Symposium, Editors), North-Holland, Amsterdam, 1974, 456 pp.
Fenstad, J.E. and Normann, D. 1974 On absolutely measurable sets, Fund. Math. 81 (1974) 91-98.
Friedman, H.M. 1971 Determinateness in the low projective hierarchy, Fund. Math. 72 (1971) 79-95.
Gale, D. and Stewart, F.M. 1953 Infinite games with perfect information, Contributions to the Theory of Games II, Ann. of Math. Studies 28 (1953) 245-266.
Gandy, R.O. 1960 Proof of Mostowski's conjecture, Bull. Acad. Polon. Sci. 8 (1960) 571-575.
Gandy, R.O. 1967 Computable functionals of finite type I, in Crossley [1967], 202-242.
Gandy, R.O. 1967a General recursive functionals of finite type and hierarchies of functions, Ann. Fac. Sci. Univ. Clermont-Ferrand 35 (1967) 5-24.
Gandy, R.O. and Yates, C.E.M. 1971 Logic Colloquium ’69 (Proceedings of the Summer School and Colloquium in Mathematical Logic, Manchester, 1969, Editors), North-Holland, Amsterdam, 1971, 451 pp.
Gödel, K. 1931 Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme, I, Monatshefte für Mathematik und Physik 38 (1931) 173-198.
Gödel, K. 1939 Consistency -proof for the generalized continuum-hypothesis, Proc. Nat. Acad. Sci. U.S.A. 25 (1939) 220-224.
Gordon, C. 1970 Comparisons between some generalizations of recursion theory, Compositio Math. 22 (1970) 333-346.
Grilliot, T.J. 1969 Selection functions for recursive functionals, Notre Dame J. of Formal Logic 10 (1969) 225-234.
Grilliot, T.J. 1969a Hierarchies based on objects of finite types, Jour. Symb. Log. 34 (1969) 177-182.
Grilliot, T.J. 1971 On effectively discontinuous type-2 objects, Jour. Symb. Log. 36 (1971) 245-248.
Grilliot, T.J. 1971a Inductive definitions and computability, Trans. Amer. Math. Soc. 158 (1971) 309-317.
Harrington, L.A. 1973 Contributions to Recursion Theory on Higher Types (or, a Proof of Harrington's Conjecture), Ph.D. thesis, MIT, 1973.
Harrington, L.A. 1974 The superjump and the first recursively Mahlo ordinal, in Fenstad-Hinman [1974], 43-52.
Harrington, L.A. 1975 Π1 2 sets and Π1 2 singletons, Proc. Amer. Math. Soc. 52 (1975) 356-360.
Harrington, L.A. 1978 Consistency and independence results in descriptive set theory, I, II, to appear in Ann. of Math.
Harrington, L.A. and Mac Queen, D.B. 1976 Selection in abstract recursion theory, Jour. Symb. Log. 41 (1976) 153-158.
Harrington, L.A. and Kechris, A.S. 1975 On characterizing Spector classes, Jour. Symb. Log. 40 (1975) 19-24.
Harrington, L.A. and Kechris, A.S. 1976 On monotone vs. non-monotone induction, Bull. Amer. Math. Soc. 82 (1976) 888-890.
Hinman, P.G. 1964 Some theorems on relative recursiveness of higher type objects (abstract), Notices Amer. Math. Soc. 11 (1964) 677.
Hinman, P.G. 1966 Ad Astra per Aspera: Hierarchy Schemata in Recursive Function Theory, Ph.D. thesis, University of California, Berkeley, 1966, 133 pp.
Hinman, P.G. 1969 Hierarchies of effective descriptive set theory, Trans. Amer. Math. Soc. 142 (1969) 111-140.
Hinman, P.G. 1969a Some applications of forcing to hierarchy problems in arithmetic, Zeitschr. f. math. Logik u. Grundlagen d. Math. 15 (1969) 341-352.
Hinman, P.G. 1973 The finite levels of the hierarchy of effective R-sets, Fund. Math. 74 (1973) 1-10.
Hinman, P.G. and Moschovakis, Y.N. 1971 Computability over the continuum, in Gandy-Yates [1971], 77-105.
Jensen, R.B. and Karp, C. 1971 Primitive recursive set functions, in Scott [1971], 143-176.
Kanger, S. 1975 Proceedings of the Third Scandinavian Logic Symposium (Uppsala, Sweden, 1973, Editor), North-Holland, Amsterdam, 1975, 214 pp.
Kantorovitch, L. and Livenson, E. 1932/33 Memoir on the analytical operations and projective sets, I and II, Fund. Math. 18 (1932) 214-279 and 20 (1933) 54-97.
Kechris, A.S. 1973 Measure and category in effective descriptive set theory, Ann. Math. Logic 5 (1973) 337-384.
Kechris, A.S. 1973a The structure of envelopes: a survey of recursion theory in higher types , MIT Logic Seminar notes, 1973, 28 pp.
Kechris, A.S. 1974 On projective ordinals, Jour. Symb. Log. 39 (1974) 269-282.
Kechris, A.S. and Moschovakis, Y.N. 1977 Recursion in higher types, in Barwise [1977], 681-737.
Kino, A. and Takeuti, G. 1962 On hierarchies of predicates of ordinal numbers, Jour. Math. Soc. Japan 14 (1962) 199-232.
Kino, A. and Takeuti, G. 1962a A note on predicates of ordinal numbers, Jour. Math. Soc. Japan 14 (1962) 367-378.
Kleene, S.C. 1935/36 General recursive functions of natural numbers, Math. Ann. 112 (1935/36) 727-742.
Kleene, S.C. 1943 Recursive predicates and quantifiers, Trans. Amer. Math. Soc. 53 (1943) 41-73.
Kleene, S.C. 1950 A symmetric form of Gödel's theorem, Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen 53 (1950) 800-802 and Indag. Math. 12 (1950) 244-246.
Kleene, S.C. 1952 Recursive functions and intuitionistic mathematics, Proceedings of the International Congress of Mathematicians, Cambridge, Mass., 1950, 679-685, American Mathematical Society, Providence, R.I., 1952.
Kleene, S.C. 1955 On the forms of the predicates in the theory of constructive ordinals (second paper), Amer. J. Math. 77 (1955) 405-428.
Kleene, S.C. 1955a Arithmetic predicates and function quantifiers, Trans. Amer. Math. Soc. 79 (1955) 312-340.
Kleene, S.C. 1955b Hierarchies of number-theoretic predicates, Bull. Amer. Math. Soc. 61 (1955) 193-213.
Kleene, S.C. 1959 Recursive functionals and quantifiers of finite types I, Trans. Amer. Math. Soc. 91 (1959) 1-52.
Kleene, S.C. 1959a Quantification of number-theoretic functions, Compos. Math. 14 (1959) 23-41.
Kleene, S.C. 1963 Recursive functionals and quantifiers of finite types II, Trans. Amer. Math. Soc. 108 (1963) 106-142.
Kondô, M. 1938 Sur l'uniformization des complémentaires analytiques et les ensembles projectifs de la seconde classe, Japanese Jour, of Math. 15 (1938) 197-230.
Kreisel, G. 1961 Set theoretic methods suggested by the notion of potential totality, in Anonymous [1961], 103-140.
Kreisel, G. 1962 The axiom of choice and the class of hyperarithmetic functions, Indag. Math. 24 (1962) 307-319.
Kreisel, G. 1971 Some reasons for generalizing recursion theory, in Gandy-Yates [1971], 139-198.
Kreisel, G. and Sacks, G.E. 1965 Metarecursive sets, Jour. Symb. Log. 30 (1965) 318-338.
Kripke, S. 1964 Transfinite recursions on admissible ordinals, I, II (abstracts), Jour. Symb. Log. 29 (1964) 161-162.
Kripke, S. 1964a Admissible ordinals and the analytic hierarchy (abstract), Jour. Symb. Log. 29 (1964) 162.
Kuratowski, K. 1966 Topology I, Academic Press, New York, 1966, 560 pp.
Lerman, M. 198? The Uppersemilattice of Degrees of Unsolvability, Perspectives in Mathematical Logic, Springer-Verlag, Berlin–Heidelberg–New York, to appear.
Lévy, A. 1963 Transfinite computability (abstract), Notices Amer. Math. Soc. 10 (1963) 286.
Lévy, A. 1965 A Hierarchy of Formulas in Set Theory, Memoirs of the Amer. Math. Soc. 57, American Mathematical Society, Providence, R.I., 1965, 76 pp.
Lévy, A. 1965a Definability in axiomatic set theory I, in Bar-Hillel [1965], 127-151.
Lévy, A. 1978 An Introduction to Set Theory, Perspectives in Mathematical Logic 3, Springer-Verlag, Berlin-Heidelberg-New York, to appear.
Ljapunov, A.A. 1949 On δs-operations preserving measurability and the property of Baire (Russian), Mat. Sbornik N.S. 24 (66) (1949) 119-127.
Ljapunov, A.A. 1953 R-Sets (Russian), Trudy Mat. Inst. Steklov. 40, Izdat Akad. Nauk SSSR, Moscow, 1953, 67 pp.
Ljapunov, A.A. 1953a On the classification of R-sets (Russian), Mat. Sbornik N.S. 32 (74) (1953) 255-262.
Ljapunov, A.A., Stschegolkow, E.A., and Arsenin, W.J. 1955 Arbeiten zur Deskriptiven Mengenlehre, Deutscher Verlag der Wissenschaften, Berlin, 1955, 108 pp.
Lorenzen, P. and Myhill, J. 1959 Constructive definition of certain analytic sets of numbers, Jour. Symb. Log. 24 (1959) 37-49.
Luzin, N. 1930 Lecons sur les Ensembles Analytiques et leurs Applications, Gauthier-Villars, Paris, 1930, 328 pp.
Machover, M. 1961 The theory of transfinite recursion, Bull. Amer. Math. Soc. 67 (1961) 575-578.
Martin, D.A. 1968 The axiom of determinateness and reduction principles in the analytical hierarchy, Bull. Amer. Math. Soc. 74 (1968) 687-689.
Martin, D.A. 1970 Measurable cardinals and analytic games, Fund. Math. 66 (1970) 287-291.
Martin, D.A. 1975 Borel determinacy, Annals of Math. 102 (1975) 363-371.
Martin, D.A. 1977 Projective sets and cardinal numbers: some questions related to the continuum problem, mimeographed, to appear revised in Jour. Symb. Log.
Martin, D.A. 1979? Borel and Projective Games, Perspectives in Mathematical Logic, Springer-Verlag, Berlin-Heidelberg-New York, to appear.
Moldestad, J. 1977 Computations in Higher Types, Lecture Notes in Mathematics 574, Springer-Verlag, Berlin-Heidelberg-New York, 1977, 203 pp.
Moschovakis, Y.N. 1967 Hyperanalytic predicates, Trans. Amer. Math. Soc. 129 (1967) 249-282.
Moschovakis, Y.N. 1969 Abstract first-order computability I, Trans. Amer. Math. Soc. 138 (1969) 427-464, II 138 (1969) 465-504.
Moschovakis, Y.N. 1969a The lack of hierarchies on the second projective class (preliminary report) (abstract), Jour. Symb. Log. 34 (1969) 155-156.
Moschovakis, Y.N. 1970 Determinacy and prewellorderings of the continuum, in Bar-Hillel [1970], 24-63.
Moschovakis, Y.N. 1970a The Suslin-Kleene theorem for countable structures, Duke Jour. Math. 37 (1970) 344-352.
Moschovakis, Y.N. 1971 Axioms for computation theories — first draft, in Gandy-Yates [1971], 199-255.
Moschovakis, Y.N. 1971a Uniformization in a playful universe, Bull. Amer. Math. Soc. 77 (1971) 731-736.
Moschovakis, Y.N. 1972 The game quantifier, Proc. Amer. Math. Soc. 31 (1972) 245-250.
Moschovakis, Y.N. 1973 Analytic definability in a playful universe, in Suppes et al. [1973], 77-85.
Moschovakis, Y.N. 1974 Elementary Induction on Abstract Structures, North-Holland, Amsterdam, 1974, 218 pp.
Moschovakis, Y.N. 1974a Structural characterizations of classes of relations, in Fenstad-Hinman [1974], 53-79.
Moschovakis, Y.N. 1974b On non-monotone inductive definability, Fund. Math. 82 (1974) 39-83.
Moschovakis, Y.N. 1978 On the basic notions in the theory of induction, to appear in the Proceedings of the Fifth International Congress for Logic, Methodology, and Philosophy of Science, London, Ontario, Canada, 1975.
Moschovakis, Y.N. 1979? Descriptive Set Theory: A Foundational Approach, North-Holland, Amsterdam, to appear.
Mostowski, A.M. 1946 On definable sets of positive integers, Fund. Math. 34 (1946) 81-112.
Mostowski, A.M. 1955 Contributions to the theory of definable sets and functions, Fund. Math. 42 (1955) 271-275.
Mostowski, A.M. 1969 Constructible Sets with Applications, North-Holland, Amsterdam 1969, 269 pp.
Müller, G.H., Oberschelp, A., and Potthoff, K. 1975 Logic Conference Kiel, 1974 (Proceedings of the International Summer Institute and Logic Colloquium, Editors), Lecture Notes in Mathematics 499, Springer-Verlag, Berlin-Heidelberg-New York, 1975, 651 pp.
Mycielski, J. 1964 On the axiom of determinateness, Fund. Math. 53 (1964) 205-224.
Mycielski, J. 1971 On some consequences of the axiom of determinateness, in Scott [1971], 265-266.
Mycielski, J. and Steinhaus, H. 1962 A mathematical axiom contradicting the axiom of choice, Bull. Acad. Polon. des Sciences 10 (1962) 1-3.
Mycielski, J. and Swierczkowski, S. 1964 On the Lebesgue measurability and the axiom of determinateness, Fund. Math. 54 (1964) 67-71.
Myhill, J. 1961 Category methods in recursion theory, Pacific Jour. Math. 11 (1961) 1479-1486.
Oxtoby, J.C. 1971 Measure and Category; A Survey of the Analogies between Topological and Measure Spaces, Springer-Verlag, Berlin-Heidelberg-New York, 1971, 95 pp.
Paris, J.B. 1972 ZF Σ0 4 determinateness, Jour. Symb. Log. 37 (1972) 661-667.
Péter, R. 1935 Konstruktion nichtrekursiver Funktionen, Math. Annalen 111 (1935) 42-60.
Péter, R. 1967 Recursive Functions, Academic Press, New York, 1967, 300 pp.
Platek, R.A. 1966 Foundations of Recursion Theory, Ph.D. thesis and supplement, Stanford University, 1966.
Post, E.L. 1944 Recursively enumerable sets of positive integers and their decision problems, Bull. Amer. Math. Soc. 50 (1944) 284-316.
Putnam, H. 1964 On hierarchies and systems of notations, Proc. Amer. Math. Soc. 15 (1964) 44-50.
Richter, W.H. 1968 Constructively accessible ordinal numbers, Jour. Symb. Log. 33 (1968) 43-55.
Richter, W.H. 1971 Recursively Mahlo ordinals and inductive definitions, in Gandy-Yates [1971], 273-288.
Richter, W.H. 1975 The least Σ1 2 and Π1 2 reflecting ordinals, in Müller et al [1975], 568-578.
Rogers, H., Jr. 1959 Recursive functions over well-ordered partial orderings, Proc. Amer. Math. Soc. 10 (1959) 847-853.
Rogers, H., Jr. 1967 Theory of Recursive Functions and Effective Computability, McGraw-Hill, New York, 1967, 482 pp.
Sacks, G.E. 1963 Degrees of Unsolvability, Annals of Math. Studies 55, Princeton Univ. Press, Princeton, 1963, 174 pp.
Sacks, G.E. 1966 Metarecursively enumerable sets and admissible ordinals, Bull. Amer. Math. Soc. 72 (1966) 59-64.
Sacks, G.E. 1966a Post's problem, admissible ordinals, and regularity, Trans. Amer. Math. Soc. 124 (1966) 1-23.
Sacks, G.E. 1967 Metarecursion theory, in Crossley [1967], 243-263.
Sacks, G.E. 1969 Measure -theoretic uniformity in recursion theory and set theory, Trans. Amer. Math. Soc. 142 (1969) 381-420.
Sacks, G.E. 1971 On the reducibility of Π1 1 sets, Advances in Math. 7 (1971) 57-82.
Sacks, G.E. 1974 The 1-section of a type-n object, in Fenstad-Hinman [1974], 81-93.
Sacks, G.E. 1978 The k-section of a type-n object, Amer. J. Math., to appear.
Sacks, G.E. and Simpson, S.G. 1972 The a-finite injury method, Ann. Math. Log. 4 (1972) 343-367.
Scott, D.S. 1971 Axiomatic Set Theory I (Proceedings of the Thirteenth Symposium in Pure Mathematics of the Amer. Math. Soc, Los Angeles, 1967, Editor), American Mathematical Society, Providence, R.I., 1971, 474 pp.
Shoenfield, J.R. 1958 The class of recursive functions, Proc. Amer. Math. Soc. 9 (1958) 690-692.
Shoenfield, J.R. 1961 The problem of predicativity, in Bar-Hillel et. al. [1961], 132-139.
Shoenfield, J.R. 1962 The form of the negation of a predicate, in Dekker [1962], 131-134.
Shoenfield, J.R. 1967 Mathematical Logic, Addison-Wesley, Reading, Mass., 1967, 344 pp.
Shoenfield, J.R. 1968 A hierarchy based on a type-2 object, Trans. Amer. Math. Soc. 134 (1968) 103-108.
Shoenfield, J.R. 1971 Unramified forcing, in Scott [1971], 357-381.
Shoenfield, J.R. 1971a Degrees of Unsolvability, North-Holland, Amsterdam, 1971, 111 pp.
Shoenfield, J.R. 1971b Measurable cardinals, in Gandy-Yates [1971], 19-49.
Shore, R.A. 1977 α-Recursion theory, in Barwise [1977].
Simpson, S.G. 1974 Degree theory on admissible ordinals, in Fenstad-Hinman [1974], 165-193.
Simpson, S.G. 1984? Admissible Recursion Theory, Perspectives in Mathematical Logic, Springer-Verlag, Berlin-Heidelberg-New York, to appear.
Solovay, R.M. 1969 On the cardinality of Σ1 2 sets of reals, in Bulloff et ai [1969], 58-73.
Spector, C. 1955 Recursive well-orderings, Jour. Symb. Log. 20 (1955) 151-163.
Spector, C. 1958 Measure -theoretic construction of incomparable hyperdegrees, Jour. Symb. Log. 23 (1958) 280-288.
Spector, C. 1959 Hyperarithmetic quantifiers, Fund. Math. 48 (1959) 313-320.
Spector, C. 1961 Inductively defined sets of natural numbers, in Anonymous [1961], 97-102.
Strong, H.R. 1968 Algebraically generalized recursive function theory, IBM Jour. Res. Devel. 12 (1968) 465-475.
Suppes, P., Henkin, L., Joja, A., and Moisil, Gr. C. 1973 Logic, Methodology, and Philosophy of Science IV (Proceedings of the Fourth International Congress for Logic, Methodology, and Philosophy of Science, Bucharest, Romania, 1971, Editors) North-Holland, Amsterdam, 1973, 981 pp.
Suzuki, Y. 1964 A complete classification of the AJ-functions, Bull. Amer. Math. Soc. 70 (1964) 246-253.
Takeuti, G. 1960 On the recursive functions of ordinal numbers, Jour. Math. Soc. of Japan 12 (1960) 119-128.
Takeuti, G. 1965 Recursive functions and arithmetic functions of ordinal numbers, in Bar-Hillel [1965], 179-196.
Tanaka, H. 1967 Some results in the effective descriptive set theory, Publ. Res. Inst. Math. Sci. Kyoto Univ., Ser. A, 3 (1967) 11-52.
Tanaka, H. 1968 A basis result for Π1 1 sets of positive measure, Comment. Math. Univ. St. Paul 16 (1968) 115-127.
Tanaka, H. 1970 On analytic well-orderings, Jour. Symb. Log. 35 (1970) 198-203.
Tanaka, H. 1970a On a n? set of positive measure, Nagoya Math. J. 38 (1970) 139-144.
Tugué, T. 1960 Predicates recursive in a type-2 object and Kleene hierarchies, Comment. Math. Univ. St. Paul 8 (1960) 97-117.
Turing, A.M. 1936 On computable numbers with an application to the Entscheidungsproblem, Proc. London Math. Soc., Series 2, 42 (1936) 230-265 and 43 (1936) 544-546.
Wagner, E.G. 1969 Uniform reflexive structures: on the nature of Gödelizations and relative computability, Trans. Amer. Math. Soc. 144 (1969) 1-41.
Zuckerman, M.M. 1974 Sets and Transfinite Numbers, Macmillan, New York, 1974, 423 pp.

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