Search results for 'Recursive Function' (try it on Scholar)

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  1.  5
    J. W. Addison (2004). Tarski's Theory of Definability: Common Themes in Descriptive Set Theory, Recursive Function Theory, Classical Pure Logic, and Finite-Universe Logic. Annals of Pure and Applied Logic 126 (1-3):77-92.
    Although the theory of definability had many important antecedents—such as the descriptive set theory initiated by the French semi-intuitionists in the early 1900s—the main ideas were first laid out in precise mathematical terms by Alfred Tarski beginning in 1929. We review here the basic notions of languages, explicit definability, and grammatical complexity, and emphasize common themes in the theories of definability for four important languages underlying, respectively, descriptive set theory, recursive function theory, classical pure logic, and finite-universe logic. (...)
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  2.  12
    H. R. Strong (1970). Construction of Models for Algebraically Generalized Recursive Function Theory. Journal of Symbolic Logic 35 (3):401-409.
    The Uniformly Reflexive Structure was introduced by E. G. Wagner who showed that the theory of such structures generalized much of recursive function theory. In this paper Uniformly Reflexive Structures are constructed as factor algebras of Free nonassociative algebras. Wagner's question about the existence of a model with no computable splinter ("successor set") is answered in the affirmative by the construction of a model whose only computable sets are the finite sets and their complements. Finally, for each countable (...)
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  3.  1
    José Félix Costa, Bruno Loff & Jerzy Mycka (2009). A Foundation for Real Recursive Function Theory. Annals of Pure and Applied Logic 160 (3):255-288.
    The class of recursive functions over the reals, denoted by , was introduced by Cristopher Moore in his seminal paper written in 1995. Since then many subsequent investigations brought new results: the class was put in relation with the class of functions generated by the General Purpose Analogue Computer of Claude Shannon; classical digital computation was embedded in several ways into the new model of computation; restrictions of were proved to represent different classes of recursive functions, e.g., (...), primitive recursive and elementary functions, and structures such as the Ritchie and the Grzergorczyk hierarchies.The class of real recursive functions was then stratified in a natural way, and and the analytic hierarchy were recently recognised as two faces of the same mathematical concept.In this new article, we bring a strong foundational support to the Real Recursive Function Theory, rooted in Mathematical Analysis, in a way that the reader can easily recognise both its intrinsic mathematical beauty and its extreme simplicity. The new paradigm is now robust and smooth enough to be taught. To achieve such a result some concepts had to change and some new results were added. (shrink)
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  4.  44
    Nigel Cutland (1980). Computability, an Introduction to Recursive Function Theory. Cambridge University Press.
    What can computers do in principle? What are their inherent theoretical limitations? These are questions to which computer scientists must address themselves. The theoretical framework which enables such questions to be answered has been developed over the last fifty years from the idea of a computable function: intuitively a function whose values can be calculated in an effective or automatic way. This book is an introduction to computability theory (or recursion theory as it is traditionally known to mathematicians). (...)
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  5.  8
    Stephen C. Kleene & Martin Davis (1990). Origins of Recursive Function Theory. Journal of Symbolic Logic 55 (1):348-350.
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  6. Stewart Shapiro (1990). Review: Stephen C. Kleene, Origins of Recursive Function Theory; Martin Davis, Why Godel Didn't Have Church's Thesis; Stephen C. Kleene, Reflections on Church's Thesis. [REVIEW] Journal of Symbolic Logic 55 (1):348-350.
     
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  7.  17
    Martin Davis (1997). Minsky ML. Size and Structure of Universal Turing Machines Using Tag Systems. Recursive Function Theory, Proceedings of Symposia in Pure Mathematics, Vol. 5, American Mathematical Society, Providence 1962, Pp. 229–238. [REVIEW] Journal of Symbolic Logic 31 (4):655-655.
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  8.  4
    Albert A. Mullin (1963). On A Theorem Equivalent to Post's Fundamental Theorem of Recursive Function Theory. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 9 (12-15):203-205.
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  9.  9
    Stewart Shapiro (1990). Kleene Stephen C.. Origins of Recursive Function Theory. Annals of the History of Computing, Vol. 3 (1981), Pp. 52–67. Davis Martin. Why Gödel Didn't Have Church's Thesis. Information and Control, Vol. 54 (1982), Pp. 3–24. Kleene Stephen C.. Reflections on Church's Thesis. Notre Dame Journal of Formal Logic, Vol. 28 (1987), Pp. 490–498. [REVIEW] Journal of Symbolic Logic 55 (1):348-350.
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  10. H. B. Enderton (1987). Review: Nigel Cutland, Computability. An Introduction to Recursive Function Theory. [REVIEW] Journal of Symbolic Logic 52 (1):292-293.
     
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  11.  3
    Joseph S. Ullian (1975). Review: Ann Yasuhara, Recursive Function Theory and Logic. [REVIEW] Journal of Symbolic Logic 40 (4):619-620.
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  12.  8
    R. L. Goodstein (1953). A Problem in Recursive Function Theory. Journal of Symbolic Logic 18 (3):225-232.
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  13.  7
    Heinrich Rolletschek (1983). Closure Properties of Almost-Finiteness Classes in Recursive Function Theory. Journal of Symbolic Logic 48 (3):756-763.
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  14.  1
    Kenneth Appel (1997). Dekker JCE. Infinite Series of Isols. Recursive Function Theory, Proceedings of Symposia in Pure Mathematics, Vol. 5, American Mathematical Society, Providence 1962, Pp. 77–96. [REVIEW] Journal of Symbolic Logic 31 (4):652-652.
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  15.  1
    Erik Ellentuck (1968). Review: John Myhill, Recursive Function Theory. [REVIEW] Journal of Symbolic Logic 33 (4):619-620.
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  16.  1
    Albert A. Mullin (1963). On A Theorem Equivalent to Post's Fundamental Theorem of Recursive Function Theory. Mathematical Logic Quarterly 9 (12‐15):203-205.
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  17. Gustav Hensel (1966). Review: H. B. Enderton, Hierarchies in Recursive Function Theory. [REVIEW] Journal of Symbolic Logic 31 (2):262-263.
     
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  18.  1
    Julia Robinson (1972). Review: Martin Davis, Application of Recursive Function Theory to Number Theory. [REVIEW] Journal of Symbolic Logic 37 (3):602-602.
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  19.  1
    Paul Young (1972). Review: Manuel Blum, Recursive Function Theory and Speed of Computation. [REVIEW] Journal of Symbolic Logic 37 (1):199-199.
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  20.  1
    J. P. Cleave (1974). Review: Webb Miller, Recursive Function Theory and Numerical Analysis. [REVIEW] Journal of Symbolic Logic 39 (2):346-346.
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  21. J. P. Cleave (1974). Miller Webb. Recursive Function Theory and Numerical Analysis. Journal of Computer and System Sciences Vol. 4 , Pp. 465–472. [REVIEW] Journal of Symbolic Logic 39 (2):346.
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  22. Erik Ellentuck (1969). Myhill John. Ω — Λ. Recursive Function Theory, Proceedings of Symposia in Pure Mathematics, Vol. 5, American Mathematical Society, Providence 1962, Pp. 97–104. [REVIEW] Journal of Symbolic Logic 33 (4):619-620.
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  23. H. B. Enderton (1987). Cutland Nigel. Computabitity. An Introduction to Recursive Function Theory. Cambridge University Press, Cambridge Etc. 1980, X + 251 Pp. [REVIEW] Journal of Symbolic Logic 52 (1):292-293.
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  24. H. B. Enderton (1971). Mullin Albert A.. On a Theorem Equivalent to Post's Fundamental Theorem of Recursive Function Theory. Zeitschrift Für Mathematische Logik Und Grundlagen der Mathematik, Vol. 9 , Pp. 203–205. [REVIEW] Journal of Symbolic Logic 36 (2):343.
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  25. H. B. Enderton (1971). Review: Albert A. Mullin, On a Theorem Equivalent to Post's Fundamental Theorem of Recursive Function Theory. [REVIEW] Journal of Symbolic Logic 36 (2):343-343.
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  26. Matthew Hassett (1967). Nerode A.. Arithmetically Isolated Sets and Nonstandard Models. Recursive Function Theory, Proceedings of Symposia in Pure Mathematics, Vol. 5, American Mathematical Society, Providence 1962, Pp. 105–116. [REVIEW] Journal of Symbolic Logic 32 (2):269.
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  27. Gustav Hensel (1966). Enderton H. B.. Hierarchies in Recursive Function Theory. Transactions of the American Mathematical Society, Vol. III , Pp. 457–471. [REVIEW] Journal of Symbolic Logic 31 (2):262-263.
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  28. Donald L. Kreider (1964). Addison J. W.. Separation Principles in the Hierarchies of Classical and Effective Descriptive Set Theory. Fundamenta Mathematicae, Vol. 46 No. 2 , Pp. 123–135.Addison J. W.. The Theory of Hierarchies. Logic, Methodology and Philosophy of Science, Proceedings of the 1960 International Congress, Edited by Nagel Ernest, Suppes Patrick, and Tarski Alfred, Stanford University Press, Stanford, Calif., 1962, Pp. 26–37.Addison J. W.. Some Problems in Hierarchy Theory. Recursive Function Theory, Proceedings of Symposia in Pure Mathematics, Vol. 5, American Mathematical Society, Providence 1962, Pp. 123–130. [REVIEW] Journal of Symbolic Logic 29 (1):60-62.
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  29. Robert McNaughton (1964). Burks A. W. And Wright J. B.. Sequence Generators and Digital Computers. Recursive Function Theory, Proceedings of Symposia in Pure Mathematics, Vol. 5, American Mathematical Society, Providence 1962, Pp. 139–199.Burks Arthur W. And Wright Jesse B.. Sequence Generators, Graphs, and Formal Languages. Information and Control, Vol. 5 , Pp. 204–212. [REVIEW] Journal of Symbolic Logic 29 (4):210-212.
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  30. John Myhill (1968). Recursive Function Theory. Journal of Symbolic Logic 33 (4):619-620.
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  31. Julia Robinson (1972). Davis Martin. Applications of Recursive Function Theory to Number Theory. Recursive Function Theory, Proceedings of Symposia in Pure Mathematics, Vol. 5, American Mathematical Society, Providence 1962, Pp. 135–138. [REVIEW] Journal of Symbolic Logic 37 (3):602.
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  32. J. A. Robinson (1968). McCarthy John. Computer Programs for Checking Mathematical Proofs. Recursive Function Theory, Proceedings of Symposia in Pure Mathematics, Vol. 5, American Mathematical Society, Providence 1962, Pp. 219–227. [REVIEW] Journal of Symbolic Logic 32 (4):523.
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  33. Norman Shapiro (1955). Myhill J. R.. Three Contributions to Recursive Function Theory. Actes du XIème Congrès International de Philosophie, Volume XIV, Volume Complémentaire Et Communications du Colloque de Logique, North-Holland Publishing Company, Amsterdam 1953, and Éditions E. Nauwelaerts, Louvain 1953, Pp. 50–59. [REVIEW] Journal of Symbolic Logic 20 (2):176-177.
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  34. Norman Shapiro (1955). Review: J. R. Myhill, Three Contributions to Recursive Function Theory. [REVIEW] Journal of Symbolic Logic 20 (2):176-177.
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  35. Ann M. Singleterry (1968). Shoenfield J. R.. The Form of the Negation of a Predicate. Recursive Function Theory, Proceedings of Symposia in Pure Mathematics, Vol. 5, American Mathematical Society, Providence 1962, Pp. 131–134. [REVIEW] Journal of Symbolic Logic 33 (1):116.
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  36. Oseph S. Ullian (1975). Yasuhara Ann. Recursive Function Theory and Logic. Academic Press, New York and London 1971, Xv + 338 Pp. [REVIEW] Journal of Symbolic Logic 40 (4):619-620.
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  37. R. E. Vesley (1967). Spector Clifford. Provably Recursive Functionals of Analysis: A Consistency Proof of Analysis by an Extension of Principles Formulated in Current Intuitionistic Mathematics. Recursive Function Theory, Proceedings of Symposia in Pure Mathematics, Vol. 5, American Mathematical Society, Providence 1962, Pp. 1–27. [REVIEW] Journal of Symbolic Logic 32 (1):128.
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  38. Paul Young (1972). Blum Manuel. Recursive Function Theory and Speed of Computation. Canadian Mathematical Bulletin , Vol. 9 , Pp. 745–750. Journal of Symbolic Logic 37 (1):199.
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  39.  13
    László Á Kóczy (2007). A Recursive Core for Partition Function Form Games. Theory and Decision 63 (1):41-51.
    We present a well-defined generalisation of the core to coalitional games with externalities, where the value of a deviation is given by an endogenous response, the solution (if nonempty: the core) of the residual game.
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  40.  6
    Mark Changizi (1996). Function Identification From Noisy Data with Recursive Error Bounds. Erkenntnis 45 (1):91 - 102.
    New success criteria of inductive inference in computational learning theory are introduced which model learning total (not necessarily recursive) functions with (possibly everywhere) imprecise theories from (possibly always) inaccurate data. It is proved that for any level of error allowable by the new success criteria, there exists a class of recursive functions such that not all f are identifiable via the criterion at that level of error. Also, necessary and sufficient conditions on the error level are given for (...)
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  41.  3
    Paul Axt (1997). Ritchie Robert W.. Classes of Recursive Functions Based on Ackermann's Function. Pacific Journal of Mathematics, Vol. 15 (1965), Pp. 1027–1044. [REVIEW] Journal of Symbolic Logic 31 (4):654-654.
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  42.  1
    Paul Axt (1966). Review: Robert W. Ritchie, Classes of Recursive Functions Based on Ackermann's Function. [REVIEW] Journal of Symbolic Logic 31 (4):654-654.
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  43. D. A. Clarke (1968). Review: Tosiyuki Tugue, On Predicates Expressible in the 1-Function Quantifier Forms in Kleene Hierarchy with Free Variables of Type 2; Tosiyuki Tugue, Predicates Recursive in a Type-2 Object and Kleene Hierarchies. [REVIEW] Journal of Symbolic Logic 33 (1):115-116.
     
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  44. D. A. Clarke (1968). Tugué Tosiyuki. On Predicates Expressible in the 1-Function Quantifier Forms in Kleene Hierarchy with Free Variables of Type 2. Proceedings of the Japan Academy, Vol. 36 , Pp. 10–14.Tugué Tosiyuki. Predicates Recursive in a Type-2 Object and Kleene Hierarchies. Commentarii Mathematici Universitatis Sancti Pauli, Vol. 8 , Pp. 97–117. [REVIEW] Journal of Symbolic Logic 33 (1):115-116.
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  45. Donald L. Kreider (1960). Dekker J. C. E. And Myhill J.. Recursive Equivalence Types. University of California Publications in Mathematics, N.S. Vol. 3 No. 3 , Pp. 67–214.Dekker J. C. E.. Congruences in Isols with a Finite Modulus. Mathematische Zeitschrift, Vol. 70 , Pp. 113–124.Myhill J.. Recursive Equivalence Types and Combinatorial Functions. Bulletin of the American Mathematical Society, Vol. 64 , Pp. 373–376.Dekker J. C. E.. The Factorial Function for Isols. Mathematische Zeitschrift, Vol. 70 , Pp. 250–262.Dekker J. C. E. And Myhill J.. The Divisibility of Isols by Powers of Primes. Mathematische Zeitschrift, Vol. 73 . Pp. 127–133.Dekker J. C. E.. An Expository Account of Isols. Summaries of Talks Presented at the Summer Institute for Symbolic Logic, Cornell University, 1957, 2nd Edn., Communications Research Division, Institute for Defense Analyses, Princeton, N.J., 1960, Pp. 189–200. [REVIEW] Journal of Symbolic Logic 25 (4):356-359.
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  46.  4
    Klaus‐Hilmar Sprenger (1997). Some Hierarchies of Primitive Recursive Functions on Term Algebras. Mathematical Logic Quarterly 43 (2):251-286.
  47.  2
    Holger Petersen (1996). The Computation of Partial Recursive Word‐Functions Without Read Instructions. Mathematical Logic Quarterly 42 (1):312-318.
    In this note we consider register-machines with symbol manipulation capabilities. They can form words over a given alphabet in their registers by appending symbols to the strings already stored. These machines are similar to Post's normal systems and the related machine-models discussed in the literature. But unlike the latter devices they are deterministic and are not allowed to read symbols from the front of the registers. Instead they can compare registers and erase them. At first glance it is surprising that (...)
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  48. Qing Zhou (1996). Computable Real‐Valued Functions on Recursive Open and Closed Subsets of Euclidean Space. Mathematical Logic Quarterly 42 (1):379-409.
    In this paper we study intrinsic notions of “computability” for open and closed subsets of Euclidean space. Here we combine together the two concepts, computability on abstract metric spaces and computability for continuous functions, and delineate the basic properties of computable open and closed sets. The paper concludes with a comprehensive examination of the Effective Riemann Mapping Theorem and related questions.
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  49.  9
    Guillaume Wunsch, Michel Mouchart & Federica Russo (2014). Functions and Mechanisms in Structural-Modelling Explanations. Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 45 (1):187-208.
    One way social scientists explain phenomena is by building structural models. These models are explanatory insofar as they manage to perform a recursive decomposition on an initial multivariate probability distribution, which can be interpreted as a mechanism. Explanations in social sciences share important aspects that have been highlighted in the mechanisms literature. Notably, spelling out the functioning the mechanism gives it explanatory power. Thus social scientists should choose the variables to include in the model on the basis of their (...)
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  50.  6
    Iraj Kalantari & Larry Welch (2004). Density and Baire Category in Recursive Topology. Mathematical Logic Quarterly 50 (4‐5):381-391.
    We develop the concepts of recursively nowhere dense sets and sets that are recursively of first category and study closed sets of points in light of Baire's Category Theorem. Our theorems are primarily concerned with exdomains of recursive quantum functions and hence with avoidable points . An avoidance function is a recursive function which can be used to expel avoidable points from domains of recursive quantum functions. We define an avoidable set of points to be (...)
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