This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aho, A.V. and Ullman, J.D. [1979] Universality of data retrieval languages, in: Proc. of 6th ACM Symp. on Principles of Programming Languages, 1979, 110–117.
Backus, J. [1978] Can programming be liberated from the von Neumann style? A functional style and its algebra of programs, Comm. of the ACM, 21 (1978), 613–641.
Barwise, J. and Moschovakis, Y.N. [1978] Global inductive definability, J. of Symbolic Logic, 43 (1978), 521–534.
Barwise, J., Gandy, R.O. and Moschovakis, Y.N. [1971] The next admissible set, J. of Symbolic Logic, 36 (1971), 108–120.
Bjoerner, D. and Jones, C.B. [1982] Formal specification and software development, Prentice-Hall, 1982.
Chandra, A. and Harel, D. [1982] Structure and complexity of computable queries, J. of Computer and System Sciences, 25 (1982), 99–128.
Chandra, A.K. and Harel, D. [1980] Computable queries for relational data bases, J. of Computer and System Sciences, 21 (1980), 156–178.
Chen, M. [1983] Space-time algorithms: semantics and methodology, Ph.D. Thesis, Cal. Inst. of Technology, 1983.
de Bakker, J. [1980] Mathematical theory of program correctness, Prentice-Hall, 1980.
de Rougemont, M. [1983] Second order and inductive definability on finite structures, Ph.D. Thesis, UCLA, 1983.
Fagin, R. [1974] Generalized first-order spectra and polynomial-time recognizible sets, in: Complexity of computation, R. Karp, ed., SIAM-AMS Proc. 7, 1974, 43–73.
Feferman, S. [1965] Some applications of forcing and generic sets, Fund. Math. 56 (1965), 325–345.
Feferman, S. [1977] Inductive schemata and recursively continuous functionals, in: Colloquium '76, R.O. Gandy, J.M.E. Hyland eds., Studies in Logic, North Holland, Amsterdam, 1977, 373–392.
Fenstad, J.-E. [1980] General recursion theory, Perspectives in Mathematical Logic, Springer, Berlin, 1980.
Friedman, H. [1971] Aiiomatic recursive function theory, in: Logic Colloquium '69, R.O. Gandy, C.E.M. Yates eds., Studies in Logic, North Holland, Amsterdam, 1971, 113–137.
Gandy, R.O. [1967] General recursive functionals of finite type and hierarchies of functionals, Ann. Fac. Sci. Univ. Clermont-Ferrand, 35, 1967, 5–24.
Gordon, M.J.C. [1979] The denotational description of programming languages, Springer, 1979.
Gurevich, Y. [1983] Algebras of feasible functions, Proc. of 24th IEEE Symp. on Foundations of Computer Science, 1983, 210–213.
Harel, D. and Kozen, D. [1982] A programming language for the inductive sets, and applications, Proc. of the 9th ICALP, Springer, 1982.
Immerman, N. [1982] Relational queries computable in polynomial time, Proc. of the 14th ACM Symp. on Theory of Computing, 1982, 147–152.
Immerman, N. [1983] Languages which capture complexity classes, Proc. of 15th ACM Symp. on the theory of computing, 1983, 347–354.
Kechris, A.S. and Moschovakis, Y.N. [1977] Recursion in higher types, in: Handbook of Logic, J. Barwise ed., Studies in Logic, North Holland, Amsterdam, 1976, 681–737.
Keisler, H.J. [1965] Finite approximations of infinitely long formulas, in: The Theory of Models, J.W. Addison et al, eds., Studies in Logic, North Holland, Amsterdam, 1965, 158–169.
Kleene, S.C. [1952] Introduction to metamathematics, van Nostrand, Princeton, 1952.
Kleene, S.C. [1959] Recursive functionals and quantifiers of finite type I, Trans. Amer. Math. Soc. 91 (1959), 1–52.
Kleene, S.C. [1963] Recursive functionals and quantifiers of finite type II, Trans. Amer. Math. Soc. 108 (1963), 106–142.
Kleene, S.C. [1981] The theory of recursive functions approaching its centennial, Bull. Amer. Math. Soc. (new series) 5 (1981), 43–61.
Kolaitis, Ph. [????] Canonical forms and hierarchies in generalized recursion theory, to appear.
Kreisel, G. [1961] Set theoretic notions suggested by the notion of potential totality, in: Infinitistic Methods, Pergamon, Oxford, 1961, 103–140.
Kreisel, G. [1965] Model theoretic invariants: applications to recursive and hyperarithmetic operations, in: The Theory of Models, J.W. Addison et al, eds., Studies in Logic, North Holland, Amsterdam, 1965.
Kreisel, G. and Sacks, G.E. [1965] Metarecursive sets, J. of Symbolic Logic, 30 (1965), 318–338.
Landin, P.J. [1964] The mechanical evaluation of expressions, Computer J. 6 (1964), 308–320.
Mc Carthy, J. [1960] Recursive functions of symbolic expressions and their computation by machine, Part I, Comm. of the ACM, 3 (1960), 184–195.
Mc Colm, G. [????] Ph.D. Thesis, UCLA, in preparation.
Mead, C. and Conway, L. [1980] Introduction to VLSI Symtems, Addison-Wesley, Reading Mass., 1980.
Moschovakis, Y.N. [1967] Hyperanalytic predicates, Trans. Amer. Math. Soc. 129 (1967), 249–282.
Moschovakis, Y.N. [1969] Abstract first order computability I and II, Trans. Amer. Math. Soc., 138 (1969), 427–504.
Moschovakis, Y.N. [1971] Axioms for computation theories — first draft, in: Logic Colloquium '69, R.O. Gandy and C.E.M. Yates eds., Studies in Logic, North Holland, Amsterdam, 1971, 199–255.
Moschovakis, Y.N. [1974] Elementary Induction on Abstract Structures, Studies in Logic, North Holland, Amsterdam, 1974.
Moschovakis, Y.N. [1977] On the basic notions on the theory of induction, in: Logic, Foundations of Mathematics and Computability, Butts, Hintikka, eds., Reidel, 1977, 207–236.
Moss, L. [1984] Power set recursion, Ph.D. Thesis, UCLA, 1984.
Normann, D. [1978] Set recursion, in: Generalized Recursion Theory II, J.-E. Fenstad, R.O. Gandy, G.E. Sacks, eds., Studies in Logic, North Holland, Amsterdam, 1978.
Platek, R. [1966] Foundations of recursion theory, Ph.D. Thesis, Standford Univ., 1966.
Rogers, H. Jr. [1967] Theory of recursive functions and effective computability, McGraw-Hill, New York, 1967.
Sacks, G.E. [1980] Three aspects of recursive enumerability, in: Recursion Theory: Its Generalizations and Applications, F.R. Drake and S.S. Wainer, eds., Cambridge Univ. Press, 1980, 184–214.
Sacks, G.E. [????] On the limits of recursive enumerability, to appear.
Sazonov, V.Y. [1980] A logical approach to the problem P = NP, Math. Found. of Comp. Science, Springer CS notes #88, 1980, 562–575.
Scott, D.S. [1982] Domains for denotational semantics, ICALP '82, Aarhus, 1982.
Scott, D.S. and Strachey, C. [1971] Towards a mathematical semantics for computer languages, Proc. of the Symposium on Computers and Automata, in: J. Fox ed., Polytechnic Institute of Brooklyn Press, New York, 1971, 19–46.
Shore, R.A. [1977] α-recursion theory, in: The Handbook of Logic, J. Barwise, ed., Studies in Logic, North Holland, Amsterdam, 1977, 653–680.
Slaman, T.A. [????] Reflection and forcing in E-recursion theory, to appear.
Stoy, J.E. [1977] Denotational semantics: The Scott-Strachey approach, MIT Press, Cambridge, Mass., 1977.
Strong, R. [1968] Algebraically generalized recursive function theory, IBM J. Res. and Dev. 12 (1968), 415–475.
Tennent, R.D. [1981] Principles of programming languages, Prentice-Hall, 1981.
Wagner, E.G. [1969] Uniform reflexive structures: on the nature of Godelizations and relative computability, Trans. Amer. Math. Soc., 144 (1969), 1–41.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1984 Springer-Verlag
About this paper
Cite this paper
Moschovakis, Y.N. (1984). Abstract recursion as a foundation for the theory of algorithms. In: Börger, E., Oberschelp, W., Richter, M.M., Schinzel, B., Thomas, W. (eds) Computation and Proof Theory. Lecture Notes in Mathematics, vol 1104. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099491
Download citation
DOI: https://doi.org/10.1007/BFb0099491
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-13901-0
Online ISBN: 978-3-540-39119-7
eBook Packages: Springer Book Archive