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Izv. Akad. Nauk SSSR Ser. Mat., 1977, Volume 41, Issue 3, Pages 483–502 (Mi izv1821)  

This article is cited in 10 scientific papers (total in 10 papers)

The nonarithmeticity of the class of realizable predicate formulas

V. E. Plisko


Abstract: It is proved that the set of Gödel numbers of realizable predicate formulas is not definable in the language of formal arithmetic.
Bibliography: 13 titles.

Full text: PDF file (1943 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Izvestiya, 1977, 11:3, 453–471

Bibliographic databases:

UDC: 517.12
MSC: Primary 02E05, 02C15, 02F99, 10N99; Secondary 02B10, 02F43, 02H15
Received: 11.06.1976

Citation: V. E. Plisko, “The nonarithmeticity of the class of realizable predicate formulas”, Izv. Akad. Nauk SSSR Ser. Mat., 41:3 (1977), 483–502; Math. USSR-Izv., 11:3 (1977), 453–471

Citation in format AMSBIB
\Bibitem{Pli77}
\by V.~E.~Plisko
\paper The nonarithmeticity of the class of realizable predicate formulas
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1977
\vol 41
\issue 3
\pages 483--502
\mathnet{http://mi.mathnet.ru/izv1821}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=476469}
\zmath{https://zbmath.org/?q=an:0373.02032|0382.03043}
\transl
\jour Math. USSR-Izv.
\yr 1977
\vol 11
\issue 3
\pages 453--471
\crossref{https://doi.org/10.1070/IM1977v011n03ABEH001731}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. E. Plisko, “Some variants of the notion of realizability for predicate formulas”, Math. USSR-Izv., 12:3 (1978), 588–604  mathnet  crossref  mathscinet  zmath
    2. V. E. Plisko, “Absolute realizability of predicate formulas”, Math. USSR-Izv., 22:2 (1984), 291–308  mathnet  crossref  mathscinet  zmath
    3. V. E. Plisko, “Modified realizability and predicate logic”, Math. Notes, 61:2 (1997), 212–220  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. V. E. Plisko, “Nachala konstruktivnoi teorii modelei”, Fundament. i prikl. matem., 8:3 (2002), 783–828  mathnet  mathscinet  zmath
    5. Albert Visser, “Substitutions of Σ10-sentences: explorations between intuitionistic propositional logic and intuitionistic arithmetic”, Annals of Pure and Applied Logic, 114:1-3 (2002), 227  crossref
    6. S. N. Artemov, “Kolmogorov and Gödel's approach to intuitionistic logic: current developments”, Russian Math. Surveys, 59:2 (2004), 203–229  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. Albert Visser, Maartje de Jonge, “No Escape from Vardanyan's theorem”, Arch Math Logic, 45:5 (2006), 539  crossref  mathscinet  zmath  isi
    8. Albert Visser, “Predicate Logics of Constructive Arithmetical Theories”, J. symb. log, 71:04 (2006), 1311  crossref
    9. Valerii E. Plisko, “A survey of predicate realizability logic”, Proc. Steklov Inst. Math., 274 (2011), 204–230  mathnet  crossref  mathscinet  isi  elib  elib
    10. A. Yu. Konovalov, “Klassicheskaya istinnost vsekh absolyutno arifmeticheski realizuemykh predikatnykh formul”, Intellektualnye sistemy. Teoriya i prilozheniya, 22:4 (2018), 111–114  mathnet
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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