Matches in SemOpenAlex for { <https://semopenalex.org/work/W2078603002> ?p ?o ?g. }
Showing items 1 to 70 of
70
with 100 items per page.
- W2078603002 endingPage "781" @default.
- W2078603002 startingPage "779" @default.
- W2078603002 abstract "Friedman has posed (see [F, p. 117]) the following problem: “35. Define the set E of expressions by (i) Con is an expression; (ii) if A, B are expressions so are (~ A ), ( A&B ), and Con( A ). Each expression ϕ in E determines a sentence ϕ in PA [classical first-order arithmetic] by taking Con* to be “ PA is consistent,” ( ~ A ) * to be ~ ( A *), ( A&B )* to be A *& B *, and Con( A )* to be “ PA + ‘ A *’ is consistent.” The set of expressions ϕ ∈ E such that ϕ* is true is recursive . The formalized second incompleteness theorem reads In order to simplify notation, we will reformulate Friedman's problem slightly. Let Con be the usual sentence of PA expressing the consistency of PA , ~ A the negation of A , ( A&B ) the conjunction of A and B , etc., and Bew( A ) the result of substituting the numeral for the Gödel number of A for the free variable in the usual provability predicate for PA . Let Con( A ) = ~ Bew(~ A ). (Con( A ) is equivalent in PA to the usual sentence expressing the consistency of PA + A .) And let the class of F-sentences be the smallest class which contains Con and which also contains ~ A , ( A&B ) and Con( A ) whenever it contains A and B . Since ⊦ PA Bew( A ) ↔ Bew( B ) if ⊦ PA A ↔ B , Friedman's problem is then the question whether the class of true F -sentences is recursive. The answer is that it is recursive. To see why, we need a definition and a theorem. Definition. An atom is a sentence Con n for some n ≥ 1, where Con t = Con and Con n + 1 = Con(Con n )." @default.
- W2078603002 created "2016-06-24" @default.
- W2078603002 creator A5008053802 @default.
- W2078603002 date "1976-12-01" @default.
- W2078603002 modified "2023-09-26" @default.
- W2078603002 title "On deciding the truth of certain statements involving the notion of consistency " @default.
- W2078603002 cites W1540715591 @default.
- W2078603002 cites W2028227692 @default.
- W2078603002 cites W2081160992 @default.
- W2078603002 doi "https://doi.org/10.2307/2272395" @default.
- W2078603002 hasPublicationYear "1976" @default.
- W2078603002 type Work @default.
- W2078603002 sameAs 2078603002 @default.
- W2078603002 citedByCount "12" @default.
- W2078603002 countsByYear W20786030022014 @default.
- W2078603002 countsByYear W20786030022019 @default.
- W2078603002 countsByYear W20786030022020 @default.
- W2078603002 crossrefType "journal-article" @default.
- W2078603002 hasAuthorship W2078603002A5008053802 @default.
- W2078603002 hasConcept C114614502 @default.
- W2078603002 hasConcept C118615104 @default.
- W2078603002 hasConcept C138885662 @default.
- W2078603002 hasConcept C140146324 @default.
- W2078603002 hasConcept C154945302 @default.
- W2078603002 hasConcept C177264268 @default.
- W2078603002 hasConcept C199360897 @default.
- W2078603002 hasConcept C2185349 @default.
- W2078603002 hasConcept C2776436953 @default.
- W2078603002 hasConcept C2777212361 @default.
- W2078603002 hasConcept C2777530160 @default.
- W2078603002 hasConcept C33923547 @default.
- W2078603002 hasConcept C41008148 @default.
- W2078603002 hasConcept C41895202 @default.
- W2078603002 hasConcept C90559484 @default.
- W2078603002 hasConceptScore W2078603002C114614502 @default.
- W2078603002 hasConceptScore W2078603002C118615104 @default.
- W2078603002 hasConceptScore W2078603002C138885662 @default.
- W2078603002 hasConceptScore W2078603002C140146324 @default.
- W2078603002 hasConceptScore W2078603002C154945302 @default.
- W2078603002 hasConceptScore W2078603002C177264268 @default.
- W2078603002 hasConceptScore W2078603002C199360897 @default.
- W2078603002 hasConceptScore W2078603002C2185349 @default.
- W2078603002 hasConceptScore W2078603002C2776436953 @default.
- W2078603002 hasConceptScore W2078603002C2777212361 @default.
- W2078603002 hasConceptScore W2078603002C2777530160 @default.
- W2078603002 hasConceptScore W2078603002C33923547 @default.
- W2078603002 hasConceptScore W2078603002C41008148 @default.
- W2078603002 hasConceptScore W2078603002C41895202 @default.
- W2078603002 hasConceptScore W2078603002C90559484 @default.
- W2078603002 hasIssue "04" @default.
- W2078603002 hasLocation W20786030021 @default.
- W2078603002 hasOpenAccess W2078603002 @default.
- W2078603002 hasPrimaryLocation W20786030021 @default.
- W2078603002 hasRelatedWork W137688234 @default.
- W2078603002 hasRelatedWork W1936960864 @default.
- W2078603002 hasRelatedWork W2011748368 @default.
- W2078603002 hasRelatedWork W2129380674 @default.
- W2078603002 hasRelatedWork W2359822642 @default.
- W2078603002 hasRelatedWork W2386521853 @default.
- W2078603002 hasRelatedWork W2626106327 @default.
- W2078603002 hasRelatedWork W3036048982 @default.
- W2078603002 hasRelatedWork W3087049664 @default.
- W2078603002 hasRelatedWork W3210968648 @default.
- W2078603002 hasVolume "41" @default.
- W2078603002 isParatext "false" @default.
- W2078603002 isRetracted "false" @default.
- W2078603002 magId "2078603002" @default.
- W2078603002 workType "article" @default.