Matches in SemOpenAlex for { <https://semopenalex.org/work/W1967050833> ?p ?o ?g. }
Showing items 1 to 80 of
80
with 100 items per page.
- W1967050833 endingPage "146" @default.
- W1967050833 startingPage "129" @default.
- W1967050833 abstract "Abstract Solovay proved the arithmetical completeness theorem for the system GL of propositional modal logic of provability. Montagna proved that this completeness does not hold for a natural extension QGL of GL to the predicate modal logic. Let Th(QGL) be the set of all theorems of QGL, Fr(QGL) be the set of all formulas valid in all transitive and conversely well-founded Kripke frames, and let PL( T ) be the set of all predicate modal formulas provable in T for any arithmetical interpretation. Montagna’s results are described as Th(QGL) ⊊ (Fr(QGL), PL(PA) ⊈ Fr(QGL), and Th(QGL) ⊊ PL(PA). In this paper, we prove the following three theorems: (1) Fr(QGL) ⊈ PL( T ) for any Σ 1 -sound recursively enumerable extension T of I Σ 1 , (2) PL( T ) ⊈ Fr(QGL) for any recursively enumerable A -theory T extending I Σ 1 , and (3) Th(QGL) ⊊ Fr(QGL) ∩ PL( T ) for any recursively enumerable A -theory T extending I Σ 2 . To prove these theorems, we use iterated consistency assertions and nonstandard models of arithmetic, and we improve Artemov’s lemma which is used to prove Vardanyan’s theorem on the Π 0 2 -completeness of PL( T )." @default.
- W1967050833 created "2016-06-24" @default.
- W1967050833 creator A5031043850 @default.
- W1967050833 date "2012-10-12" @default.
- W1967050833 modified "2023-10-16" @default.
- W1967050833 title "ARITHMETICAL INTERPRETATIONS AND KRIPKE FRAMES OF PREDICATE MODAL LOGIC OF PROVABILITY" @default.
- W1967050833 cites W1572451808 @default.
- W1967050833 cites W1977396974 @default.
- W1967050833 cites W2005337919 @default.
- W1967050833 cites W2059933820 @default.
- W1967050833 cites W2073543470 @default.
- W1967050833 cites W2076792546 @default.
- W1967050833 cites W2079626851 @default.
- W1967050833 cites W2094842664 @default.
- W1967050833 cites W4253934133 @default.
- W1967050833 cites W4291166496 @default.
- W1967050833 doi "https://doi.org/10.1017/s1755020312000275" @default.
- W1967050833 hasPublicationYear "2012" @default.
- W1967050833 type Work @default.
- W1967050833 sameAs 1967050833 @default.
- W1967050833 citedByCount "3" @default.
- W1967050833 countsByYear W19670508332013 @default.
- W1967050833 countsByYear W19670508332021 @default.
- W1967050833 crossrefType "journal-article" @default.
- W1967050833 hasAuthorship W1967050833A5031043850 @default.
- W1967050833 hasConcept C112343008 @default.
- W1967050833 hasConcept C114092440 @default.
- W1967050833 hasConcept C118615104 @default.
- W1967050833 hasConcept C136119220 @default.
- W1967050833 hasConcept C140146324 @default.
- W1967050833 hasConcept C160131679 @default.
- W1967050833 hasConcept C185592680 @default.
- W1967050833 hasConcept C188027245 @default.
- W1967050833 hasConcept C192609573 @default.
- W1967050833 hasConcept C199360897 @default.
- W1967050833 hasConcept C200116569 @default.
- W1967050833 hasConcept C202444582 @default.
- W1967050833 hasConcept C203702658 @default.
- W1967050833 hasConcept C27508121 @default.
- W1967050833 hasConcept C33923547 @default.
- W1967050833 hasConcept C41008148 @default.
- W1967050833 hasConcept C71139939 @default.
- W1967050833 hasConceptScore W1967050833C112343008 @default.
- W1967050833 hasConceptScore W1967050833C114092440 @default.
- W1967050833 hasConceptScore W1967050833C118615104 @default.
- W1967050833 hasConceptScore W1967050833C136119220 @default.
- W1967050833 hasConceptScore W1967050833C140146324 @default.
- W1967050833 hasConceptScore W1967050833C160131679 @default.
- W1967050833 hasConceptScore W1967050833C185592680 @default.
- W1967050833 hasConceptScore W1967050833C188027245 @default.
- W1967050833 hasConceptScore W1967050833C192609573 @default.
- W1967050833 hasConceptScore W1967050833C199360897 @default.
- W1967050833 hasConceptScore W1967050833C200116569 @default.
- W1967050833 hasConceptScore W1967050833C202444582 @default.
- W1967050833 hasConceptScore W1967050833C203702658 @default.
- W1967050833 hasConceptScore W1967050833C27508121 @default.
- W1967050833 hasConceptScore W1967050833C33923547 @default.
- W1967050833 hasConceptScore W1967050833C41008148 @default.
- W1967050833 hasConceptScore W1967050833C71139939 @default.
- W1967050833 hasIssue "1" @default.
- W1967050833 hasLocation W19670508331 @default.
- W1967050833 hasOpenAccess W1967050833 @default.
- W1967050833 hasPrimaryLocation W19670508331 @default.
- W1967050833 hasRelatedWork W1967050833 @default.
- W1967050833 hasRelatedWork W2019813941 @default.
- W1967050833 hasRelatedWork W2079626851 @default.
- W1967050833 hasRelatedWork W2623438580 @default.
- W1967050833 hasRelatedWork W2990466353 @default.
- W1967050833 hasRelatedWork W3119769598 @default.
- W1967050833 hasRelatedWork W3168366845 @default.
- W1967050833 hasRelatedWork W4287393491 @default.
- W1967050833 hasRelatedWork W4306181908 @default.
- W1967050833 hasRelatedWork W1800724283 @default.
- W1967050833 hasVolume "6" @default.
- W1967050833 isParatext "false" @default.
- W1967050833 isRetracted "false" @default.
- W1967050833 magId "1967050833" @default.
- W1967050833 workType "article" @default.