Results for 'Computability'

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  1.  10
    Computer Science Logic: 11th International Workshop, CSL'97, Annual Conference of the EACSL, Aarhus, Denmark, August 23-29, 1997, Selected Papers.M. Nielsen, Wolfgang Thomas & European Association for Computer Science Logic - 1998 - Springer Verlag.
    This book constitutes the strictly refereed post-workshop proceedings of the 11th International Workshop on Computer Science Logic, CSL '97, held as the 1997 Annual Conference of the European Association on Computer Science Logic, EACSL, in Aarhus, Denmark, in August 1997. The volume presents 26 revised full papers selected after two rounds of refereeing from initially 92 submissions; also included are four invited papers. The book addresses all current aspects of computer science logics and its applications and thus presents the state (...)
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  2. Paul M. kjeldergaard.Pittsburgh Computations Centers - 1968 - In T. Dixon & Deryck Horton, Verbal Behavior and General Behavior Theory. Prentice-Hall.
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  3.  22
    Hector freytes, Antonio ledda, Giuseppe sergioli and.Roberto Giuntini & Probabilistic Logics in Quantum Computation - 2013 - In Hanne Andersen, Dennis Dieks, Wenceslao J. Gonzalez, Thomas Uebel & Gregory Wheeler, New Challenges to Philosophy of Science. Springer Verlag. pp. 49.
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  4. Randomness and Recursive Enumerability.Siam J. Comput - unknown
    One recursively enumerable real α dominates another one β if there are nondecreasing recursive sequences of rational numbers (a[n] : n ∈ ω) approximating α and (b[n] : n ∈ ω) approximating β and a positive constant C such that for all n, C(α − a[n]) ≥ (β − b[n]). See [R. M. Solovay, Draft of a Paper (or Series of Papers) on Chaitin’s Work, manuscript, IBM Thomas J. Watson Research Center, Yorktown Heights, NY, 1974, p. 215] and [G. J. (...)
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  5. The fortieth annual lecture series 1999-2000.Brain Computations & an Inevitable Conflict - 2000 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 31:199-200.
  6.  9
    A Model for Proustian Decay.Computer Lars - 2024 - Nordic Journal of Aesthetics 33 (67).
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  7. The general problem of the primitive was finally solved in 1912 by A. Den-joy. But his integration process was more complicated than that of Lebesgue. Denjoy's basic idea was to first calculate the definite integral∫ b. [REVIEW]How to Compute Antiderivatives - 1995 - Bulletin of Symbolic Logic 1 (3).
     
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  8. Section 2. Model Theory.Va Vardanyan, On Provability Resembling Computability, Proving Aa Voronkov & Constructive Logic - 1989 - In Jens Erik Fenstad, Ivan Timofeevich Frolov & Risto Hilpinen, Logic, methodology, and philosophy of science VIII: proceedings of the Eighth International Congress of Logic, Methodology, and Philosophy of Science, Moscow, 1987. New York, NY, U.S.A.: Sole distributors for the U.S.A. and Canada, Elsevier Science.
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  9. Computability and recursion.Robert I. Soare - 1996 - Bulletin of Symbolic Logic 2 (3):284-321.
    We consider the informal concept of "computability" or "effective calculability" and two of the formalisms commonly used to define it, "(Turing) computability" and "(general) recursiveness". We consider their origin, exact technical definition, concepts, history, general English meanings, how they became fixed in their present roles, how they were first and are now used, their impact on nonspecialists, how their use will affect the future content of the subject of computability theory, and its connection to other related areas. (...)
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  10.  28
    Computability theory, nonstandard analysis, and their connections.Dag Normann & Sam Sanders - 2019 - Journal of Symbolic Logic 84 (4):1422-1465.
    We investigate the connections between computability theory and Nonstandard Analysis. In particular, we investigate the two following topics and show that they are intimately related. A basic property of Cantor space$2^ $ is Heine–Borel compactness: for any open covering of $2^ $, there is a finite subcovering. A natural question is: How hard is it to compute such a finite subcovering? We make this precise by analysing the complexity of so-called fan functionals that given any $G:2^ \to $, output (...)
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  11.  4
    Intentional identity revisited.Ahti Pietarinen A. School of Cognitive, Computing Sciences, Falmer, Brighton, BN1 9QH & Uk - 2010 - Nordic Journal of Philosophical Logic 6 (2):147-188.
    The problem of intentional identity, as originally offered by Peter Geach, says that there can be an anaphoric link between an indefinite term and a pronoun across a sentential boundary and across propositional attitude contexts, where the actual existence of an individual for the indefinite term is not presupposed. In this paper, a semantic resolution to this elusive puzzle is suggested, based on a new quantified intensional logic and game-theoretic semantics (GTS) of imperfect information. This constellation leads to an expressive (...)
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  12.  7
    A logical formalisation of false belief tasks.R. Velázquez-Quesada A. Institute for Logic Anthia Solaki Fernando, Computation Language, Netherlandsb Netherlands Organization for Applied Scientific Research, Media Studies Netherlandsc Information Science & Norway - forthcoming - Journal of Applied Non-Classical Logics:1-51.
    Theory of Mind (ToM), the cognitive capacity to attribute internal mental states to oneself and others, is a crucial component of social skills. Its formal study has become important, witness recent research on reasoning and information update by intelligent agents, and some proposals for its formal modelling have put forward settings based on Epistemic Logic (EL). Still, due to intrinsic idealisations, it is questionable whether EL can be used to model the high-order cognition of ‘real’ agents. This manuscript proposes a (...)
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  13. Computability, Notation, and de re Knowledge of Numbers.Stewart Shapiro, Eric Snyder & Richard Samuels - 2022 - Philosophies 1 (7):20.
    Saul Kripke once noted that there is a tight connection between computation and de re knowledge of whatever the computation acts upon. For example, the Euclidean algorithm can produce knowledge of which number is the greatest common divisor of two numbers. Arguably, algorithms operate directly on syntactic items, such as strings, and on numbers and the like only via how the numbers are represented. So we broach matters of notation. The purpose of this article is to explore the relationship between (...)
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  14. Computability theory and differential geometry.Robert I. Soare - 2004 - Bulletin of Symbolic Logic 10 (4):457-486.
    Let M be a smooth, compact manifold of dimension n ≥ 5 and sectional curvature | K | ≤ 1. Let Met (M) = Riem(M)/Diff(M) be the space of Riemannian metrics on M modulo isometries. Nabutovsky and Weinberger studied the connected components of sublevel sets (and local minima) for certain functions on Met (M) such as the diameter. They showed that for every Turing machine T e , e ∈ ω, there is a sequence (uniformly effective in e) of homology (...)
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  15.  56
    Computability Theory: An Introduction to Recursion Theory.Herbert B. Enderton - 2010 - Academic Press.
    Machine generated contents note: 1. The Computability Concept;2. General Recursive Functions;3. Programs and Machines;4. Recursive Enumerability;5. Connections to Logic;6. Degrees of Unsolvability;7. Polynomial-Time Computability;Appendix: Mathspeak;Appendix: Countability;Appendix: Decadic Notation;.
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  16.  31
    Computability and the game of cops and robbers on graphs.Rachel D. Stahl - 2022 - Archive for Mathematical Logic 61 (3):373-397.
    Several results about the game of cops and robbers on infinite graphs are analyzed from the perspective of computability theory. Computable robber-win graphs are constructed with the property that no computable robber strategy is a winning strategy, and such that for an arbitrary computable ordinal \, any winning strategy has complexity at least \}\). Symmetrically, computable cop-win graphs are constructed with the property that no computable cop strategy is a winning strategy. Locally finite infinite trees and graphs are explored. (...)
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  17.  54
    Computability and analysis: the legacy of Alan Turing.Jeremy Avigad & Vasco Brattka - unknown
    We discuss the legacy of Alan Turing and his impact on computability and analysis.
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  18. (1 other version)Computability and Logic.G. S. Boolos & R. C. Jeffrey - 1977 - British Journal for the Philosophy of Science 28 (1):95-95.
     
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  19. Constructivism, Computability, and Physical Theories.Wayne C. Myrvold - 1994 - Dissertation, Boston University
    This dissertation is an investigation into the degree to which the mathematics used in physical theories can be constructivized. The techniques of recursive function theory and classical logic are used to separate out the algorithmic content of mathematical theories rather than attempting to reformulate them in terms of "intuitionistic" logic. The guiding question is: are there experimentally testable predictions in physics which are not computable from the data? ;The nature of Church's thesis, that the class of effectively calculable functions on (...)
     
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  20. Computability Results Used in Differential Geometry.Barbara F. Csima & Robert I. Soare - 2006 - Journal of Symbolic Logic 71 (4):1394 - 1410.
    Topologists Nabutovsky and Weinberger discovered how to embed computably enumerable (c.e.) sets into the geometry of Riemannian metrics modulo diffeomorphisms. They used the complexity of the settling times of the c.e. sets to exhibit a much greater complexity of the depth and density of local minima for the diameter function than previously imagined. Their results depended on the existence of certain sequences of c.e. sets, constructed at their request by Csima and Soare, whose settling times had the necessary dominating properties. (...)
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  21. Computability, Complexity and Languages.Martin Davies, Ron Segal & Elaine Weyuker - 1994 - Academic Press.
     
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  22.  36
    Computability Theory.Daniele Mundici & Wilfried Sieg - unknown
    Daniele Mundici and Wilfred Sieg. Computability Theory.
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  23.  58
    Conditional computability of real functions with respect to a class of operators.Ivan Georgiev & Dimiter Skordev - 2013 - Annals of Pure and Applied Logic 164 (5):550-565.
    For any class of operators which transform unary total functions in the set of natural numbers into functions of the same kind, we define what it means for a real function to be uniformly computable or conditionally computable with respect to this class. These two computability notions are natural generalizations of certain notions introduced in a previous paper co-authored by Andreas Weiermann and in another previous paper by the same authors, respectively. Under certain weak assumptions about the class in (...)
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  24.  93
    Computability, consciousness, and algorithms.Robert Wilensky - 1990 - Behavioral and Brain Sciences 13 (4):690-691.
  25. Kurt Gödel and Computability Theory.Richard Zach - 2006 - In Beckmann Arnold, Berger Ulrich, Löwe Benedikt & Tucker John V., Logical Approaches to Computational Barriers. Second Conference on Computability in Europe, CiE 2006, Swansea. Proceedings. Springer. pp. 575--583.
    Although Kurt Gödel does not figure prominently in the history of computabilty theory, he exerted a significant influence on some of the founders of the field, both through his published work and through personal interaction. In particular, Gödel’s 1931 paper on incompleteness and the methods developed therein were important for the early development of recursive function theory and the lambda calculus at the hands of Church, Kleene, and Rosser. Church and his students studied Gödel 1931, and Gödel taught a seminar (...)
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  26. (1 other version)Computability and λ-definability.A. M. Turing - 1937 - Journal of Symbolic Logic 2 (4):153-163.
  27.  17
    On notions of computability-theoretic reduction between Π21 principles.Denis R. Hirschfeldt & Carl G. Jockusch - 2016 - Journal of Mathematical Logic 16 (1):1650002.
    Several notions of computability-theoretic reducibility between [Formula: see text] principles have been studied. This paper contributes to the program of analyzing the behavior of versions of Ramsey’s Theorem and related principles under these notions. Among other results, we show that for each [Formula: see text], there is an instance of RT[Formula: see text] all of whose solutions have PA degree over [Formula: see text] and use this to show that König’s Lemma lies strictly between RT[Formula: see text] and RT[Formula: (...)
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  28.  59
    Physical Computation: A Mechanistic Account.Gualtiero Piccinini - 2015 - Oxford, GB: Oxford University Press UK.
    Gualtiero Piccinini articulates and defends a mechanistic account of concrete, or physical, computation. A physical system is a computing system just in case it is a mechanism one of whose functions is to manipulate vehicles based solely on differences between different portions of the vehicles according to a rule defined over the vehicles. Physical Computation discusses previous accounts of computation and argues that the mechanistic account is better. Many kinds of computation are explicated, such as digital vs. analog, serial vs. (...)
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  29.  44
    Computational Artifacts: Towards a Philosophy of Computer Science.Raymond Turner - 2018 - Springer Berlin Heidelberg.
    The philosophy of computer science is concerned with issues that arise from reflection upon the nature and practice of the discipline of computer science. This book presents an approach to the subject that is centered upon the notion of computational artefact. It provides an analysis of the things of computer science as technical artefacts. Seeing them in this way enables the application of the analytical tools and concepts from the philosophy of technology to the technical artefacts of computer science. With (...)
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  30. Computability Theory.Barry Cooper - 2010 - Journal of the Indian Council of Philosophical Research 27 (1).
     
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  31.  66
    The veblen functions for computability theorists.Alberto Marcone & Antonio Montalbán - 2011 - Journal of Symbolic Logic 76 (2):575 - 602.
    We study the computability-theoretic complexity and proof-theoretic strength of the following statements: (1) "If X is a well-ordering, then so is ε X ", and (2) "If X is a well-ordering, then so is φ(α, X)", where α is a fixed computable ordinal and φ represents the two-placed Veblen function. For the former statement, we show that ω iterations of the Turing jump are necessary in the proof and that the statement is equivalent to ${\mathrm{A}\mathrm{C}\mathrm{A}}_{0}^{+}$ over RCA₀. To prove (...)
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  32.  60
    Computability of Recursive Functions.J. C. Shepherdson & H. E. Sturgis - 1967 - Journal of Symbolic Logic 32 (1):122-123.
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  33.  42
    Computability. Computable Functions, Logic, and the Foundations of Mathematics.Richard L. Epstein & Walter A. Carnielli - 2002 - Bulletin of Symbolic Logic 8 (1):101-104.
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  34.  43
    Towards applied theories based on computability logic.Giorgi Japaridze - 2010 - Journal of Symbolic Logic 75 (2):565-601.
    Computability logic (CL) is a recently launched program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth that logic has more traditionally been. Formulas in it represent computational problems, "truth" means existence of an algorithmic solution, and proofs encode such solutions. Within the line of research devoted to finding axiomatizations for ever more expressive fragments of CL, the present paper introduces a new deductive system CL12 and proves its soundness and (...)
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  35.  29
    (1 other version)Computability, Proof, and Open-Texture.Stewart Shapiro - 2006 - In Adam Olszewski, Jan Wolenski & Robert Janusz, Church's Thesis After 70 Years. Ontos Verlag. pp. 420-455.
  36. Computability theory and linear orders.Rod Downey - 1998 - In I︠U︡riĭ Leonidovich Ershov, Handbook of recursive mathematics. New York: Elsevier. pp. 138--823.
     
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  37. Counterpossibles in Science: The Case of Relative Computability.Matthias Jenny - 2018 - Noûs 52 (3):530-560.
    I develop a theory of counterfactuals about relative computability, i.e. counterfactuals such as 'If the validity problem were algorithmically decidable, then the halting problem would also be algorithmically decidable,' which is true, and 'If the validity problem were algorithmically decidable, then arithmetical truth would also be algorithmically decidable,' which is false. These counterfactuals are counterpossibles, i.e. they have metaphysically impossible antecedents. They thus pose a challenge to the orthodoxy about counterfactuals, which would treat them as uniformly true. What’s more, (...)
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  38. A natural axiomatization of computability and proof of Church’s thesis.Nachum Dershowitz & Yuri Gurevich - 2008 - Bulletin of Symbolic Logic 14 (3):299-350.
    Church's Thesis asserts that the only numeric functions that can be calculated by effective means are the recursive ones, which are the same, extensionally, as the Turing-computable numeric functions. The Abstract State Machine Theorem states that every classical algorithm is behaviorally equivalent to an abstract state machine. This theorem presupposes three natural postulates about algorithmic computation. Here, we show that augmenting those postulates with an additional requirement regarding basic operations gives a natural axiomatization of computability and a proof of (...)
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  39.  11
    Proceedings of the 1986 Conference on Theoretical Aspects of Reasoning about Knowledge: March 19-22, 1988, Monterey, California.Joseph Y. Halpern, International Business Machines Corporation, American Association of Artificial Intelligence, United States & Association for Computing Machinery - 1986
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  40. Computability and Logic.George Boolos, John Burgess, Richard P. & C. Jeffrey - 1980 - New York: Cambridge University Press. Edited by John P. Burgess & Richard C. Jeffrey.
    Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the staple topics of an intermediate logic course, such as Godel's incompleteness theorems, but also a large number of optional topics, from Turing's theory of computability to Ramsey's theorem. This 2007 fifth edition has been thoroughly revised by John Burgess. Including a selection of exercises, adjusted for this edition, at the end of each chapter, it (...)
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  41. Randomness and computability: Open questions.Joseph S. Miller & André Nies - 2006 - Bulletin of Symbolic Logic 12 (3):390-410.
    It is time for a new paper about open questions in the currently very active area of randomness and computability. Ambos-Spies and Kučera presented such a paper in 1999 [1]. All the question in it have been solved, except for one: is KL-randomness different from Martin-Löf randomness? This question is discussed in Section 6.Not all the questions are necessarily hard—some simply have not been tried seriously. When we think a question is a major one, and therefore likely to be (...)
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  42.  48
    Introduction to computability logic.Giorgi Japaridze - 2003 - Annals of Pure and Applied Logic 123 (1-3):1-99.
    This work is an attempt to lay foundations for a theory of interactive computation and bring logic and theory of computing closer together. It semantically introduces a logic of computability and sets a program for studying various aspects of that logic. The intuitive notion of computational problems is formalized as a certain new, procedural-rule-free sort of games between the machine and the environment, and computability is understood as existence of an interactive Turing machine that wins the game against (...)
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  43.  24
    Degrees of randomized computability.Rupert Hölzl & Christopher P. Porter - 2022 - Bulletin of Symbolic Logic 28 (1):27-70.
    In this survey we discuss work of Levin and V’yugin on collections of sequences that are non-negligible in the sense that they can be computed by a probabilistic algorithm with positive probability. More precisely, Levin and V’yugin introduced an ordering on collections of sequences that are closed under Turing equivalence. Roughly speaking, given two such collections $\mathcal {A}$ and $\mathcal {B}$, $\mathcal {A}$ is below $\mathcal {B}$ in this ordering if $\mathcal {A}\setminus \mathcal {B}$ is negligible. The degree structure associated (...)
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  44. Godel on computability.W. Sieg - 2006 - Philosophia Mathematica 14 (2):189-207.
    The identification of an informal concept of ‘effective calculability’ with a rigorous mathematical notion like ‘recursiveness’ or ‘Turing computability’ is still viewed as problematic, and I think rightly so. I analyze three different and conflicting perspectives Gödel articulated in the three decades from 1934 to 1964. The significant shifts in Gödel's position underline the difficulties of the methodological issues surrounding the Church-Turing Thesis.
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  45.  20
    Unconventional Computing, Arts, Philosophy.Andrew Adamatzky (ed.) - 2022 - World Scientific Publishing Company.
    The unique compendium re-assesses the value of future and emergent computing technologies via artistic and philosophical means. The book encourages scientists to adopt inspiring thinking of artists and philosophers to reuse scientific concepts in their works.The useful reference text consists of non-typical topics, where artistic and philosophical concepts encourage readers to adopt unconventional approaches towards computing and immerse themselves into discoveries of future emerging landscape.
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  46.  41
    Computable analysis of the abstract Cauchy problem in a Banach space and its applications I.Klaus Weihrauch & Ning Zhong - 2007 - Mathematical Logic Quarterly 53 (4‐5):511-531.
    We study computability of the abstract linear Cauchy problem equation image)where A is a linear operator, possibly unbounded, on a Banach space X. We give necessary and sufficient conditions for A such that the solution operator K: x ↦ u of the problem is computable. For studying computability we use the representation approach to computable analysis developed by Weihrauch and others. This approach is consistent with the model used by Pour-El/Richards.
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  47.  27
    The dependence of computability on numerical notations.Ethan Brauer - 2021 - Synthese 198 (11):10485-10511.
    Which function is computed by a Turing machine will depend on how the symbols it manipulates are interpreted. Further, by invoking bizarre systems of notation it is easy to define Turing machines that compute textbook examples of uncomputable functions, such as the solution to the decision problem for first-order logic. Thus, the distinction between computable and uncomputable functions depends on the system of notation used. This raises the question: which systems of notation are the relevant ones for determining whether a (...)
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  48.  96
    Reverse mathematics, computability, and partitions of trees.Jennifer Chubb, Jeffry L. Hirst & Timothy H. McNicholl - 2009 - Journal of Symbolic Logic 74 (1):201-215.
    We examine the reverse mathematics and computability theory of a form of Ramsey's theorem in which the linear n-tuples of a binary tree are colored.
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  49.  14
    Computation Structures.Stephen A. Ward & Robert H. Halstead - 1990 - McGraw-Hill.
    Developed as the text for the basic computer architecture course at MIT, Computation Structures integrates a thorough coverage of digital logic design with a comprehensive presentation of computer architecture.
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  50.  79
    Copeland and Proudfoot on computability.Michael Rescorla - 2012 - Studies in History and Philosophy of Science Part A 43 (1):199-202.
    Many philosophers contend that Turing’s work provides a conceptual analysis of numerical computability. In (Rescorla, 2007), I dissented. I argued that the problem of deviant notations stymies existing attempts at conceptual analysis. Copeland and Proudfoot respond to my critique. I argue that their putative solution does not succeed. We are still awaiting a genuine conceptual analysis.
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