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Mathematicians --- Logic, symbolic and mathematical. --- Gentzen, Gerhard.

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Logic. --- Logic, Symbolic and mathematical. --- Modality (Logic). --- Gentzen, Gerhard,

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Provability, Computability and Reflection

Logic, Symbolic and mathematical. --- Mathematics --- Logique symbolique et mathématique --- Mathématiques --- EPUB-LIV-FT ELSEVIER-B --- Metamathematics. --- Logic, Symbolic and mathematical --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Philosophy --- 510.6 --- 510.6 Mathematical logic --- Gentzen, Gerhard --- Oeuvres --- Écrits. --- Written works. --- Logic, symbolic and mathematical --- Logique mathématique --- Gentzen, Gerhard.

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Gerhard Gentzen has been described as logic’s lost genius, whom Gödel called a better logician than himself. This work comprises articles by leading proof theorists, attesting to Gentzen’s enduring legacy to mathematical logic and beyond. The contributions range from philosophical reflections and re-evaluations of Gentzen’s original consistency proofs to the most recent developments in proof theory. Gentzen founded modern proof theory. His sequent calculus and natural deduction system beautifully explain the deep symmetries of logic. They underlie modern developments in computer science such as automated theorem proving and type theory. .

Computer science. --- Mathematical Theory --- Mathematics --- Physical Sciences & Mathematics --- Proof theory --- Data processing. --- Gentzen, Gerhard. --- Mathematics. --- Mathematical logic. --- Mathematical Logic and Foundations. --- Mathematical Logic and Formal Languages. --- Logic, Symbolic and mathematical. --- Informatics --- Science --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism

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The information age owes its existence to a little-known but crucial development, the theoretical study of logic and the foundations of mathematics. The Great Formal Machinery Works draws on original sources and rare archival materials to trace the history of the theories of deduction and computation that laid the logical foundations for the digital revolution.Jan von Plato examines the contributions of figures such as Aristotle; the nineteenth-century German polymath Hermann Grassmann; George Boole, whose Boolean logic would prove essential to programming languages and computing; Ernst Schröder, best known for his work on algebraic logic; and Giuseppe Peano, cofounder of mathematical logic. Von Plato shows how the idea of a formal proof in mathematics emerged gradually in the second half of the nineteenth century, hand in hand with the notion of a formal process of computation. A turning point was reached by 1930, when Kurt Gödel conceived his celebrated incompleteness theorems. They were an enormous boost to the study of formal languages and computability, which were brought to perfection by the end of the 1930s with precise theories of formal languages and formal deduction and parallel theories of algorithmic computability. Von Plato describes how the first theoretical ideas of a computer soon emerged in the work of Alan Turing in 1936 and John von Neumann some years later.Shedding new light on this crucial chapter in the history of science, The Great Formal Machinery Works is essential reading for students and researchers in logic, mathematics, and computer science.

Information technology --- Computers --- History. --- Arend Heyting. --- Begriffsschrift. --- Bertrand Russell. --- David Hilbert. --- Earth. --- Ernst Schröder. --- Eugenio Beltrami. --- Gentzen. --- George Boole. --- Gerard Gentzen. --- Gottlob Frege. --- Guiseppe Peano. --- Gödel. --- Göttingen. --- Hermann Grassmann. --- Heyting algebras. --- Hilbert. --- Karl Menger. --- Kurt Gödel. --- Kurt Hensel. --- Leopold Kronecker. --- Moritz Schlick. --- Paul Bernays. --- Peano. --- Principia Mathematica. --- Rudolf Carnap. --- Thoralf Skolem. --- Vienna Circle. --- algebraic equations. --- algebraic logic. --- algorithmic computability. --- angles. --- arithmetic. --- assumptions. --- axioms. --- basic notions. --- calculus. --- classical arithmetic. --- computation. --- connectives. --- contemporary logic. --- deduction. --- deductive reasoning. --- digital revolution. --- finitary reasoning. --- finitism. --- geometry. --- hypothetic reasoning. --- incompleteness theorems. --- indirect proofs. --- inference. --- information age. --- intuistic arithmetic. --- lattice theory. --- logic. --- logical empiricism. --- logical structure. --- logical truths. --- mathematical logic. --- mathematical proofs. --- mathematical roots. --- mathematics. --- negation. --- non-Euclidan geometries. --- notation. --- one-place predicates. --- parallel postulate. --- philosophy. --- programming language. --- proof. --- pure thinking. --- quantificational inferences. --- theorems. --- triangles.