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- Systems_of_Logic_Based_on_Ordinals abstract "Systems of Logic Based on Ordinals was the PhD dissertation of the mathematician Alan Turing.The thesis is an exploration of formal mathematical systems after Gödel's theorem. Gödel showed for that any formal system S powerful enough to represent arithmetic, there is a theorem G which is true but the system is unable to prove. G could be added as an additional axiom to the system in place of a proof. However this would create a new system S' with its own unprovable true theorem G', and so on. Turing's thesis considers iterating the process to infinity, creating a system with an infinite set of axioms.The thesis was completed at Princeton under Alonzo Church and was a classic work in mathematics which introduced the concept of ordinal logic.Martin Davis states that although Turing's use of a computing oracle is not a major focus of the dissertation, it has proven to be highly influential in theoretical computer science, e.g. in the polynomial time hierarchy.".
- Systems_of_Logic_Based_on_Ordinals wikiPageExternalLink turingnotices.pdf.
- Systems_of_Logic_Based_on_Ordinals wikiPageExternalLink dissertation.
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- Systems_of_Logic_Based_on_Ordinals wikiPageWikiLink Alan_Turing.
- Systems_of_Logic_Based_on_Ordinals wikiPageWikiLink Alonzo_Church.
- Systems_of_Logic_Based_on_Ordinals wikiPageWikiLink Category:Alan_Turing.
- Systems_of_Logic_Based_on_Ordinals wikiPageWikiLink Category:History_of_logic.
- Systems_of_Logic_Based_on_Ordinals wikiPageWikiLink Category:Ordinal_numbers.
- Systems_of_Logic_Based_on_Ordinals wikiPageWikiLink Category:Systems_of_formal_logic.
- Systems_of_Logic_Based_on_Ordinals wikiPageWikiLink Gxc3xb6dels_incompleteness_theorems.
- Systems_of_Logic_Based_on_Ordinals wikiPageWikiLink Martin_Davis.
- Systems_of_Logic_Based_on_Ordinals wikiPageWikiLink Mathematician.
- Systems_of_Logic_Based_on_Ordinals wikiPageWikiLink Oracle_machine.
- Systems_of_Logic_Based_on_Ordinals wikiPageWikiLink Ordinal_logic.
- Systems_of_Logic_Based_on_Ordinals wikiPageWikiLink Polynomial_hierarchy.
- Systems_of_Logic_Based_on_Ordinals wikiPageWikiLink Polynomial_time_hierarchy.
- Systems_of_Logic_Based_on_Ordinals wikiPageWikiLink Theoretical_computer_science.
- Systems_of_Logic_Based_on_Ordinals wikiPageWikiLinkText "Systems of Logic Based on Ordinals".
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- Systems_of_Logic_Based_on_Ordinals subject Category:Alan_Turing.
- Systems_of_Logic_Based_on_Ordinals subject Category:History_of_logic.
- Systems_of_Logic_Based_on_Ordinals subject Category:Ordinal_numbers.
- Systems_of_Logic_Based_on_Ordinals subject Category:Systems_of_formal_logic.
- Systems_of_Logic_Based_on_Ordinals hypernym Dissertation.
- Systems_of_Logic_Based_on_Ordinals type Book.
- Systems_of_Logic_Based_on_Ordinals type Scientist.
- Systems_of_Logic_Based_on_Ordinals type Scientist.
- Systems_of_Logic_Based_on_Ordinals comment "Systems of Logic Based on Ordinals was the PhD dissertation of the mathematician Alan Turing.The thesis is an exploration of formal mathematical systems after Gödel's theorem. Gödel showed for that any formal system S powerful enough to represent arithmetic, there is a theorem G which is true but the system is unable to prove. G could be added as an additional axiom to the system in place of a proof.".
- Systems_of_Logic_Based_on_Ordinals label "Systems of Logic Based on Ordinals".
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- Systems_of_Logic_Based_on_Ordinals sameAs Q7663875.
- Systems_of_Logic_Based_on_Ordinals sameAs Q7663875.
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- Systems_of_Logic_Based_on_Ordinals isPrimaryTopicOf Systems_of_Logic_Based_on_Ordinals.