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  1. Completeness in the Theory of Types.Leon Henkin - 1950 - Journal of Symbolic Logic 15 (2):81-91.
  • Introduction to a General Theory of Elementary Propositions.Emil L. Post - 1921 - American Journal of Mathematics 43 (3):163--185.
    In the general theory of logic built up by Whitehead and Russell to furnish a basis for all mathematics there is a certain subtheory which is unique in its simplicity and precision; and though all other portions of the work have their roots in this subtheory, it itself is completely independent of them. Whereas the complete theory requires for the enunciation of its propositions real and apparent variables, which represent both individuals and propositional functions of different kinds, and as a (...)
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  • Handbook of Philosophical Logic.Dov M. Gabbay & Franz Guenthner (eds.) - 1989 - Kluwer Academic Publishers.
    The first edition of the Handbook of Philosophical Logic (four volumes) was published in the period 1983-1989 and has proven to be an invaluable reference work ...
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  • Mathematical Logic as Based on the Theory of Types.Bertrand Russell - 1908 - American Journal of Mathematics 30 (3):222-262.
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  • From Frege to Gödel: A Source Book in Mathematical Logic, 1879--1931.J. van Heijenoort (ed.) - 1967 - Harvard University Press.
  • The Mathematical Work of S. C. Kleene.J. R. Shoenfield & S. C. Kleene - 1995 - Bulletin of Symbolic Logic 1 (1):8-43.
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  • The Calculi of Lambda-Conversion.Barkley Rosser - 1941 - Journal of Symbolic Logic 6 (4):171-171.
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  • Principia Mathematica.Morris R. Cohen - 1912 - Philosophical Review 21 (1):87.
  • The Completeness of the First-Order Functional Calculus.Leon Henkin - 1949 - Journal of Symbolic Logic 14 (3):159-166.
  • Identity as a Logical Primitive.Leon Henkin - 1975 - Philosophia 5 (1-2):31-45.
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  • Computability and Logic.George Boolos, John Burgess, Richard P. & C. Jeffrey - 2007 - Cambridge University Press.
    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. Including a selection of exercises, adjusted for this edition, at the end of each chapter, it offers a new and simpler treatment of the representability of recursive functions, a (...)
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  • Mathematical Logic.Stephen Cole Kleene - 1967 - Dover Publications.
    Undergraduate students with no prior classroom instruction in mathematical logic will benefit from this evenhanded multipart text by one of the centuries greatest authorities on the subject. Part I offers an elementary but thorough overview of mathematical logic of first order. The treatment does not stop with a single method of formulating logic; students receive instruction in a variety of techniques, first learning model theory (truth tables), then Hilbert-type proof theory, and proof theory handled through derived rules. Part II supplements (...)
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  • Introduction to Mathematical Logic.ALONZO CHURCH - 1944 - London: Oxford University PRess.
    This book is intended to be used as a textbook by students of mathematics, and also within limitations as a reference work.
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  • A Formulation of the Simple Theory of Types.Alonzo Church - 1940 - Journal of Symbolic Logic 5 (2):56-68.
  • Computability and Λ-Definability.A. M. Turing - 1937 - Journal of Symbolic Logic 2 (4):153-163.
  • A Note on the Entscheidungsproblem.Alonzo Church - 1936 - Journal of Symbolic Logic 1 (1):40-41.
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  • Some Theorems on Definability and Decidability.Alonzo Church & W. V. Quine - 1952 - Journal of Symbolic Logic 17 (3):179-187.
  • A Formulation of the Logic of Sense and Denotation. [REVIEW]Rulon Wells - 1952 - Journal of Symbolic Logic 17 (2):133-134.
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  • An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof.M. Yasuhara & Peter B. Andrews - 1988 - Journal of Symbolic Logic 53 (1):312.
  • American Logic in the 1920s.Martin Davis - 1995 - Bulletin of Symbolic Logic 1 (3):273-278.
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  • The Discovery of My Completeness Proofs.Leon Henkin - 1996 - Bulletin of Symbolic Logic 2 (2):127-158.
  • Alan Turing.Andrew Hodges - 2000 - Minds and Machines.
  • Undecidable Theories.Alfred Tarski - 1968 - Amsterdam: North-Holland Pub. Co..
    This book is well known for its proof that many mathematical systems - including lattice theory and closure algebras - are undecidable. It consists of three treatises from one of the greatest logicians of all time: "A General Method in Proofs of Undecidability," "Undecidability and Essential Undecidability in Mathematics," and "Undecidability of the Elementary Theory of Groups.".
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  • The Calculi of Lambda-Conversion.Alonzo Church - 1941 - Princeton University Press.
  • Alan Turing: The Enigma.Andrew Hodges - 1985 - Journal of Symbolic Logic 50 (4):1065-1067.
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  • A Note on the Entscheidungs Problem.Alonzo Church - 1936 - Journal of Symbolic Logic 1 (2):74-74.
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  • A Formulation of the Simple Theory of Types.Alonzo Church - 1940 - Journal of Symbolic Logic 5 (3):114-115.
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  • Introduction to Metamathematics.Stephen Cole Kleene - 1952 - North Holland.
  • Classical Recursion Theory: The Theory of Functions and Sets of Natural Numbers.Piergiorgio Odifreddi - 1989 - Sole Distributors for the Usa and Canada, Elsevier Science Pub. Co..
    Volume II of Classical Recursion Theory describes the universe from a local (bottom-up or synthetical) point of view, and covers the whole spectrum, from the recursive to the arithmetical sets. The first half of the book provides a detailed picture of the computable sets from the perspective of Theoretical Computer Science. Besides giving a detailed description of the theories of abstract Complexity Theory and of Inductive Inference, it contributes a uniform picture of the most basic complexity classes, ranging from small (...)
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  • From Frege to Gödel.[author unknown] - 1968 - Philosophical Books 9 (1):31-32.
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  • Handbook of Philosophical Logic.D. M. Gabbay & F. Guenthner - 2007 - Bulletin of Symbolic Logic 13 (2):248-250.
     
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  • Undecidable Theories.Alfred Tarski - 1959 - British Journal for the Philosophy of Science 9 (36):321-327.
     
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  • On Computable Numbers, with an Application to the Entscheidungsproblem.Alan Turing - 1936 - Proceedings of the London Mathematical Society 42 (1):230-265.
  • A Note on Recursive Functions.S. C. Kleene - 1936 - Journal of Symbolic Logic 1 (3):119-119.
  • Formal Definitions in the Theory of Ordinal Numbers.Alonzo Church & S. C. Kleene - 1937 - Journal of Symbolic Logic 2 (2):87-87.
  • Review: Augustus de Morgan, On the Syllogism and Other Logical Writings by Augustus de Morgan. [REVIEW]Alonzo Church - 1976 - Journal of Symbolic Logic 41 (2):546-547.
  • Alternatives to Zermelo's Assumption.Alonzo Church - 1927 - New York.
  • Mathematical Logic.Joseph R. Shoenfield - 1967 - Reading, Mass., Addison-Wesley Pub. Co..
  • The Lambda Calculus: Its Syntax and Semantics.H. P. Barendregt - 1984 - Elsevier.
    The revised edition contains a new chapter which provides an elegant description of the semantics. The various classes of lambda calculus models are described in a uniform manner. Some didactical improvements have been made to this edition. An example of a simple model is given and then the general theory (of categorical models) is developed. Indications are given of those parts of the book which can be used to form a coherent course.
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  • General Recursive Functions of Natural Numbers.S. C. Kleene - 1937 - Journal of Symbolic Logic 2 (1):38-38.
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  • Algorithms and Decision Problems: A Crash Course in Recursion Theory.Dirk van Dalen - 1989 - Journal of Symbolic Logic 54 (3):1094-1095.
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  • The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems, and Computable Functions.Martin Davis (ed.) - 1965 - Dover Publication.
    "A valuable collection both for original source material as well as historical formulations of current problems."-- The Review of Metaphysics "Much more than a mere collection of papers . . . a valuable addition to the literature."-- Mathematics of Computation An anthology of fundamental papers on undecidability and unsolvability by major figures in the field, this classic reference opens with Godel's landmark 1931 paper demonstrating that systems of logic cannot admit proofs of all true assertions of arithmetic. Subsequent papers by (...)
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  • The Universal Turing Machine. A Half-Century Survey.Rolf Herken - 1992 - Revue Philosophique de la France Et de l'Etranger 182 (3):344-350.
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  • A Theory of Propositional Types.Leon Henkin - 1963 - Fundamenta Mathematicae 52:323-334.
     
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  • Origins of Recursive Function Theory.Stephen C. Kleene & Martin Davis - 1990 - Journal of Symbolic Logic 55 (1):348-350.
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  • An Unsolvable Problem of Elementary Number Theory.Alonzo Church - 1936 - Journal of Symbolic Logic 1 (2):73-74.
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  • Extensions of First Order Logic.María Manzano - 1996 - Cambridge University Press.
    Classical logic has proved inadequate in various areas of computer science, artificial intelligence, mathematics, philosopy and linguistics. This is an introduction to extensions of first-order logic, based on the principle that many-sorted logic (MSL) provides a unifying framework in which to place, for example, second-order logic, type theory, modal and dynamic logics and MSL itself. The aim is two fold: only one theorem-prover is needed; proofs of the metaproperties of the different existing calculi can be avoided by borrowing them from (...)
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