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- Gentzens_consistency_proof abstract "Gentzen's consistency proof is a result of proof theory in mathematical logic, published by Gerhard Gentzen in 1936. It shows that the Peano axioms of first-order arithmetic do not contain a contradiction (i.e. are \"consistent\"), as long as a certain other system used in the proof does not contain any contradictions either. This other system, today called \"primitive recursive arithmetic with the additional principle of quantifier-free transfinite induction up to the ordinal ε0\", is neither weaker nor stronger than the system of Peano axioms. Gentzen argued that it avoids the questionable modes of inference contained in Peano arithmetic and that its consistency is therefore less controversial.".
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- Gentzens_consistency_proof wikiPageExternalLink Kurt_Gödel_Collected_Works_Volume_III.html?id=gDzbuUwma5MC&pg=PA87.
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- Gentzens_consistency_proof wikiPageRevisionID "696718916".
- Gentzens_consistency_proof wikiPageWikiLink Annals_of_Mathematics.
- Gentzens_consistency_proof wikiPageWikiLink Association_for_Symbolic_Logic.
- Gentzens_consistency_proof wikiPageWikiLink Category:Metatheorems.
- Gentzens_consistency_proof wikiPageWikiLink Category:Proof_theory.
- Gentzens_consistency_proof wikiPageWikiLink Consistency.
- Gentzens_consistency_proof wikiPageWikiLink Epsilon_numbers_(mathematics).
- Gentzens_consistency_proof wikiPageWikiLink Factorial.
- Gentzens_consistency_proof wikiPageWikiLink Fibonacci_number.
- Gentzens_consistency_proof wikiPageWikiLink Gerhard_Gentzen.
- Gentzens_consistency_proof wikiPageWikiLink Goodsteins_theorem.
- Gentzens_consistency_proof wikiPageWikiLink Gxc3xb6dels_incompleteness_theorems.
- Gentzens_consistency_proof wikiPageWikiLink Hermann_Weyl.
- Gentzens_consistency_proof wikiPageWikiLink Jeff_Paris.
- Gentzens_consistency_proof wikiPageWikiLink Laurence_Kirby.
- Gentzens_consistency_proof wikiPageWikiLink London_Mathematical_Society.
- Gentzens_consistency_proof wikiPageWikiLink Mathematical_logic.
- Gentzens_consistency_proof wikiPageWikiLink Natural_number.
- Gentzens_consistency_proof wikiPageWikiLink Ordinal_analysis.
- Gentzens_consistency_proof wikiPageWikiLink Ordinal_notation.
- Gentzens_consistency_proof wikiPageWikiLink Ordinal_number.
- Gentzens_consistency_proof wikiPageWikiLink Paul_Bernays.
- Gentzens_consistency_proof wikiPageWikiLink Peano_axioms.
- Gentzens_consistency_proof wikiPageWikiLink Primitive_recursive_arithmetic.
- Gentzens_consistency_proof wikiPageWikiLink Primitive_recursive_function.
- Gentzens_consistency_proof wikiPageWikiLink Proof_theory.
- Gentzens_consistency_proof wikiPageWikiLink Quantifier_(logic).
- Gentzens_consistency_proof wikiPageWikiLink Recursion.
- Gentzens_consistency_proof wikiPageWikiLink Recursive_set.
- Gentzens_consistency_proof wikiPageWikiLink Transfinite_induction.
- Gentzens_consistency_proof wikiPageWikiLink Tree_(graph_theory).
- Gentzens_consistency_proof wikiPageWikiLink Well-order.
- Gentzens_consistency_proof wikiPageWikiLink Wilhelm_Ackermann.
- Gentzens_consistency_proof wikiPageWikiLinkText "Gentzen's consistency proof".
- Gentzens_consistency_proof wikiPageWikiLinkText "Gentzen's proof".
- Gentzens_consistency_proof wikiPageWikiLinkText "Gentzen's theorem".
- Gentzens_consistency_proof wikiPageWikiLinkText "consistency proof".
- Gentzens_consistency_proof wikiPageWikiLinkText "proof of the consistency of Peano arithmetic".
- Gentzens_consistency_proof wikiPageWikiLinkText "proved the consistency".
- Gentzens_consistency_proof wikiPageWikiLinkText "shown".
- Gentzens_consistency_proof wikiPageUsesTemplate Template:Citation.
- Gentzens_consistency_proof wikiPageUsesTemplate Template:Cite_book.
- Gentzens_consistency_proof wikiPageUsesTemplate Template:Harv.
- Gentzens_consistency_proof wikiPageUsesTemplate Template:Harvid.
- Gentzens_consistency_proof wikiPageUsesTemplate Template:Harvtxt.
- Gentzens_consistency_proof wikiPageUsesTemplate Template:Reflist.
- Gentzens_consistency_proof subject Category:Metatheorems.
- Gentzens_consistency_proof subject Category:Proof_theory.
- Gentzens_consistency_proof hypernym Result.
- Gentzens_consistency_proof type Proof.
- Gentzens_consistency_proof type Theorem.
- Gentzens_consistency_proof comment "Gentzen's consistency proof is a result of proof theory in mathematical logic, published by Gerhard Gentzen in 1936. It shows that the Peano axioms of first-order arithmetic do not contain a contradiction (i.e. are \"consistent\"), as long as a certain other system used in the proof does not contain any contradictions either.".
- Gentzens_consistency_proof label "Gentzen's consistency proof".
- Gentzens_consistency_proof sameAs Q5533794.
- Gentzens_consistency_proof sameAs m.0bgwt8.
- Gentzens_consistency_proof sameAs Q5533794.
- Gentzens_consistency_proof wasDerivedFrom Gentzens_consistency_proof?oldid=696718916.
- Gentzens_consistency_proof isPrimaryTopicOf Gentzens_consistency_proof.