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2011, ISBN: 1156574587
ID: 13945275550
[EAN: 9781156574584], Neubuch, [PU: Reference Series Books Llc Nov 2011], MATHEMATICS / LOGIC, This item is printed on demand - Print on Demand Titel. Neuware - Source: Wikipedia. Pages: 88. Chapters: Mathematical induction, Presburger arithmetic, Gödel's completeness theorem, Soundness, Natural deduction, Original proof of Gödel's completeness theorem, Consistency, Gödel's incompleteness theorems, Curry-Howard correspondence, Mathematical fallacy, Reverse mathematics, Sequent calculus, Large countable ordinal, Hilbert system, Deduction theorem, Fast-growing hierarchy, Ordinal notation, O-consistent theory, Decidability, Undecidable problem, Hilbert's program, Metalanguage, Extension by definitions, Ordinal analysis, Veblen function, Dialectica interpretation, Gödel-Gentzen negative translation, Pure type system, Herbrand's theorem, Cut-elimination theorem, Bounded quantifier, Slow-growing hierarchy, Gentzen's consistency proof, Elementary function arithmetic, Realizability, Conservative extension, Formal proof, Setoid, Lambda-mu calculus, Primitive recursive functional, Hardy hierarchy, Epsilon calculus, Peano-Russell notation, Independence, Analytic proof, Structural proof theory, Turnstile, Judgment, Proof calculus, Friedman translation, Self-verifying theories, Structural rule, Bachmann-Howard ordinal, Proof-theoretic semantics, Provability logic, Disjunction and existence properties, Conservativity theorem, Paraconsistent mathematics, Deep inference, Psi0(Omega omega), Takeuti's conjecture, Deductive system, Geometry of interaction, Tolerant sequence, Weak interpretability, Proof procedure, Decidable sublanguages of set theory, Feferman-Schütte ordinal, Church-Kleene ordinal, Proof mining, Completeness of atomic initial sequents, Proof net, VIPER microprocessor, NuPRL, Reverse reconstruction. Excerpt: Gödel's incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems capable of doing mathematics. The theorems, proven by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The two results are widely interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all of mathematics is impossible, thus giving a negative answer to Hilbert's second problem. The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an 'effective procedure' (essentially, a computer program) is capable of proving all facts about the natural numbers. For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem shows that if such a system is also capable of proving certain basic facts about the natural numbers, then one particular arithmetic truth the system cannot prove is the consistency of the system itself. Because statements of a formal theory are written in symbolic form, it is possible to mechanically verify that a formal proof from a finite set of axioms is valid. This task, known as automatic proof verification, is closely related to automated theorem proving. The difference is that instead of constructing a new proof, the proof verifier simply checks that a provided formal proof (or, in some cases, instructions that can be followed to create a formal proof) is correct. This process is not merely hypothetical; systems such as Isabelle are used today to formalize proofs and then check their validity. Many theories of interest include an infinite set of axioms, however. To verify a formal . 88 pp. Englisch
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2010, ISBN: 9781156574584
[ED: Pappeinband], [PU: Bertrams Print On Demand], - Source: Wikipedia. Pages: 88. Chapters: Mathematical induction, Presburger arithmetic, Gödel's completeness theorem, Soundness, Natural deduction, Original proof of Gödel's completeness theorem, Consistency, Gödel's incompleteness theorems, Curry-Howard correspondence, Mathematical fallacy, Reverse mathematics, Sequent calculus, Large countable ordinal, Hilbert system, Deduction theorem, Fast-growing hierarchy, Ordinal notation, O-consistent theory, Decidability, Undecidable problem, Hilbert's program, Metalanguage, Extension by definitions, Ordinal analysis, Veblen function, Dialectica interpretation, Gödel-Gentzen negative translation, Pure type system, Herbrand's theorem, Cut-elimination theorem, Bounded quantifier, Slow-growing hierarchy, Gentzen's consistency proof, Elementary function arithmetic, Realizability, Conservative extension, Formal proof, Setoid, Lambda-mu calculus, Primitive recursive functional, Hardy hierarchy, Epsilon calculus, Peano-Russell notation, Independence, Analytic proof, Structural proof theory, Turnstile, Judgment, Proof calculus, Friedman translation, Self-verifying theories, Structural rule, Bachmann-Howard ordinal, Proof-theoretic semantics, Provability logic, Disjunction and existence properties, Conservativity theorem, Paraconsistent mathematics, Deep inference, Psi0(Omega omega), Takeuti's conjecture, Deductive system, Geometry of interaction, Tolerant sequence, Weak interpretability, Proof procedure, Decidable sublanguages of set theory, Feferman-Schütte ordinal, Church-Kleene ordinal, Proof mining, Completeness of atomic initial sequents, Proof net, VIPER microprocessor, NuPRL, Reverse reconstruction. Excerpt: Gödel's incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems capable of doing mathematics. The theorems, proven by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The two results are widely interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all of mathematics is impossible, thus giving a negative answer to Hilbert's second problem. The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (essentially, a computer program) is capable of proving all facts about the natural numbers. For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem shows that if such a system is also capable of proving certain basic facts about the natural numbers, then one particular arithmetic truth the system cannot prove is the consistency of the system itself. Because statements of a formal theory are written in symbolic form, it is possible to mechanically verify that a formal proof from a finite set of axioms is valid. This task, known as automatic proof verification, is closely related to automated theorem proving. The difference is that instead of constructing a new proof, the proof verifier simply checks that a provided formal proof (or, in some cases, instructions that can be followed to create a formal proof) is correct. This process is not merely hypothetical systems such as Isabelle are used today to formalize proofs and then check their validity. Many theories of interest include an infinite set of axioms, however. To verify a formal ... - Besorgungstitel - vorauss. Lieferzeit 3-5 Tage.., [SC: 0.00]
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ISBN: 9781156574584
[ED: Taschenbuch], [PU: Books LLC, Reference Series], Source: Wikipedia. Pages: 88. Chapters: Mathematical induction, Presburger arithmetic, Gödel's completeness theorem, Soundness, Natural deduction, Original proof of Gödel's completeness theorem, Consistency, Gödel's incompleteness theorems, Curry-Howard correspondence, Mathematical fallacy, Reverse mathematics, Sequent calculus, Large countable ordinal, Hilbert system, Deduction theorem, Fast-growing hierarchy, Ordinal notation, O-consistent theory, Decidability, Undecidable problem, Hilbert's program, Metalanguage, Extension by definitions, Ordinal analysis, Veblen function, Dialectica interpretation, Gödel-Gentzen negative translation, Pure type system, Herbrand's theorem, Cut-elimination theorem, Bounded quantifier, Slow-growing hierarchy, Gentzen's consistency proof, Elementary function arithmetic, Realizability, Conservative extension, Formal proof, Setoid, Lambda-mu calculus, Primitive recursive functional, Hardy hierarchy, Epsilon calculus, Peano-Russell notation, Independence, Analytic proof, Structural proof theory, Turnstile, Judgment, Proof calculus, Friedman translation, Self-verifying theories, Structural rule, Bachmann-Howard ordinal, Proof-theoretic semantics, Provability logic, Disjunction and existence properties, Conservativity theorem, Paraconsistent mathematics, Deep inference, Psi0(Omega omega), Takeuti's conjecture, Deductive system, Geometry of interaction, Tolerant sequence, Weak interpretability, Proof procedure, Decidable sublanguages of set theory, Feferman-Schütte ordinal, Church-Kleene ordinal, Proof mining, Completeness of atomic initial sequents, Proof net, VIPER microprocessor, NuPRL, Reverse reconstruction. Excerpt: Gödel's incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems capable of doing mathematics. The theorems, proven by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The two results are widely interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all of mathematics is impossible, thus giving a negative answer to Hilbert's second problem. The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an "effective procedure" (essentially, a computer program) is capable of proving all facts about the natural numbers. For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem shows that if such a system is also capable of proving certain basic facts about the natural numbers, then one particular arithmetic truth the system cannot prove is the consistency of the system itself. Because statements of a formal theory are written in symbolic form, it is possible to mechanically verify that a formal proof from a finite set of axioms is valid. This task, known as automatic proof verification, is closely related to automated theorem proving. The difference is that instead of constructing a new proof, the proof verifier simply checks that a provided formal proof (or, in some cases, instructions that can be followed to create a formal proof) is correct. This process is not merely hypothetical systems such as Isabelle are used today to formalize proofs and then check their validity. Many theories of interest include an infinite set of axioms, however. To verify a formal ...Versandfertig in 3-5 Tagen, [SC: 0.00]
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1931, ISBN: 9781156574584
[ED: Taschenbuch], [PU: Books LLC, Reference Series], Source: Wikipedia. Pages: 88. Chapters: Mathematical induction, Presburger arithmetic, Gödel's completeness theorem, Soundness, Natural deduction, Original proof of Gödel's completeness theorem, Consistency, Gödel's incompleteness theorems, Curry-Howard correspondence, Mathematical fallacy, Reverse mathematics, Sequent calculus, Large countable ordinal, Hilbert system, Deduction theorem, Fast-growing hierarchy, Ordinal notation, O-consistent theory, Decidability, Undecidable problem, Hilbert's program, Metalanguage, Extension by definitions, Ordinal analysis, Veblen function, Dialectica interpretation, Gödel-Gentzen negative translation, Pure type system, Herbrand's theorem, Cut-elimination theorem, Bounded quantifier, Slow-growing hierarchy, Gentzen's consistency proof, Elementary function arithmetic, Realizability, Conservative extension, Formal proof, Setoid, Lambda-mu calculus, Primitive recursive functional, Hardy hierarchy, Epsilon calculus, Peano-Russell notation, Independence, Analytic proof, Structural proof theory, Turnstile, Judgment, Proof calculus, Friedman translation, Self-verifying theories, Structural rule, Bachmann-Howard ordinal, Proof-theoretic semantics, Provability logic, Disjunction and existence properties, Conservativity theorem, Paraconsistent mathematics, Deep inference, Psi0(Omega omega), Takeuti's conjecture, Deductive system, Geometry of interaction, Tolerant sequence, Weak interpretability, Proof procedure, Decidable sublanguages of set theory, Feferman-Schütte ordinal, Church-Kleene ordinal, Proof mining, Completeness of atomic initial sequents, Proof net, VIPER microprocessor, NuPRL, Reverse reconstruction. Excerpt: Gödel's incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems capable of doing mathematics. The theorems, proven by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The two results are widely interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all of mathematics is impossible, thus giving a negative answer to Hilbert's second problem. The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an "effective procedure" (essentially, a computer program) is capable of proving all facts about the natural numbers. For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem shows that if such a system is also capable of proving certain basic facts about the natural numbers, then one particular arithmetic truth the system cannot prove is the consistency of the system itself. Because statements of a formal theory are written in symbolic form, it is possible to mechanically verify that a formal proof from a finite set of axioms is valid. This task, known as automatic proof verification, is closely related to automated theorem proving. The difference is that instead of constructing a new proof, the proof verifier simply checks that a provided formal proof (or, in some cases, instructions that can be followed to create a formal proof) is correct. This process is not merely hypothetical systems such as Isabelle are used today to formalize proofs and then check their validity. Many theories of interest include an infinite set of axioms, however. To verify a formal ...Versandfertig in 3-5 Tagen, [SC: 0.00]
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2010, ISBN: 1156574587, Lieferbar binnen 4-6 Wochen Versandkosten:Versandkostenfrei innerhalb der BRD
ID: 9781156574584
Internationaler Buchtitel. In englischer Sprache. Verlag: Books LLC, 344 Seiten, L=152mm, B=229mm, H=20mm, Gew.=513gr, Kartoniert/Broschiert
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Titel: | Proof Theory: Godel's Incompleteness Theorems |
ISBN-Nummer: | 1156574587 |
Detailangaben zum Buch - Proof Theory: Godel's Incompleteness Theorems
EAN (ISBN-13): 9781156574584
ISBN (ISBN-10): 1156574587
Taschenbuch
Erscheinungsjahr: 2010
Herausgeber: Books LLC
344 Seiten
Gewicht: 0,513 kg
Sprache: eng/Englisch
Buch in der Datenbank seit 04.06.2011 02:22:14
Buch zuletzt gefunden am 01.10.2014 04:03:54
ISBN/EAN: 1156574587
ISBN - alternative Schreibweisen:
1-156-57458-7, 978-1-156-57458-4
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