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  1.  19
    Eine Variante zur Dialectica-Interpretation der Heyting-Arithmetik endlicher Typen.Justus Diller - 1974 - Archive for Mathematical Logic 16 (1-2):49-66.
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  2.  11
    Simultane Rekursionen in der Theorie der Funktionale endlicher Typen.Justus Diller & Kurt Schütte - 1971 - Archive for Mathematical Logic 14 (1-2):69-74.
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  3.  30
    Logical problems of functional interpretations.Justus Diller - 2002 - Annals of Pure and Applied Logic 114 (1-3):27-42.
    Gödel interpreted Heyting arithmetic HA in a “logic-free” fragment T 0 of his theory T of primitive recursive functionals of finite types by his famous Dialectica-translation D . This works because the logic of HA is extremely simple. If the logic of the interpreted system is different—in particular more complicated—, it forces us to look for different and more complicated functional translations. We discuss the arising logical problems for arithmetical and set theoretical systems from HA to CZF . We want (...)
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  4.  11
    Functional interpretations.Justus Diller - 2020 - New Jersey: World Scientific.
    This book gives a detailed treatment of functional interpretations of arithmetic, analysis, and set theory. The subject goes back to Gödel's Dialectica interpretation of Heyting arithmetic which replaces nested quantification by higher type operations and thus reduces the consistency problem for arithmetic to the problem of computability of primitive recursive functionals of finite types. Regular functional interpretations, i.e. Dialectica and Diller-Nahm interpretation as well as Kreisel's modified realization, together with their Troelstra-style hybrids, are applied to constructive as well as classical (...)
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  5.  40
    Functional interpretations of constructive set theory in all finite types.Justus Diller - 2008 - Dialectica 62 (2):149–177.
    Gödel's dialectica interpretation of Heyting arithmetic HA may be seen as expressing a lack of confidence in our understanding of unbounded quantification. Instead of formally proving an implication with an existential consequent or with a universal antecedent, the dialectica interpretation asks, under suitable conditions, for explicit 'interpreting' instances that make the implication valid. For proofs in constructive set theory CZF-, it may not always be possible to find just one such instance, but it must suffice to explicitly name a set (...)
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  6.  17
    Functional Interpretations of Constructive Set Theory in All Finite Types.Justus Diller - 2008 - Dialectica 62 (2):149-177.
    Gödel's dialectica interpretation of Heyting arithmetic HA may be seen as expressing a lack of confidence in our understanding of unbounded quantification. Instead of formally proving an implication with an existential consequent or with a universal antecedent, the dialectica interpretation asks, under suitable conditions, for explicit ‘interpreting’ instances that make the implication valid. For proofs in constructive set theory CZF‐, it may not always be possible to find just one such instance, but it must suffice to explicitly name a set (...)
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  7.  6
    Functional Interpretations of Classical and Constructive Set Theory.Justus Diller - 2012 - In Ulrich Berger, Hannes Diener, Peter Schuster & Monika Seisenberger (eds.), Logic, Construction, Computation. De Gruyter. pp. 137-156.
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  8.  8
    Functional Interpretations of Classical Systems.Justus Diller - 2010 - In Ralf Schindler (ed.), Ways of Proof Theory. De Gruyter. pp. 241-256.
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  9.  15
    Nicht‐persistenz der parallelität in affinen ebenen.Justus Diller - 1969 - Mathematical Logic Quarterly 15 (26‐29):431-433.
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  10.  29
    Nicht‐Persistenz der Parallelität in Affinen Ebenen.Justus Diller - 1969 - Mathematical Logic Quarterly 15 (26-29):431-433.
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  11. Rekursionstheorie: vierstündige Vorlesung.Justus Diller - 1976 - Münster i. W.: Westfälische Wilhelms-Universität, Institut für mathematische Logik und Grundlagenforschung.
     
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  12.  7
    Wolfram Pohlers—Life and Work.Justus Diller - 2010 - In Ralf Schindler (ed.), Ways of Proof Theory. De Gruyter. pp. 1-6.
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  13.  25
    Journal of Soviet Mathematics.G. E. Mints, U. V. Matiasevic, A. O. Slisenko, Justus Diller & Martin Stein - 1987 - Journal of Symbolic Logic 52 (2):561-561.
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  14.  9
    ISILC Proof Theory Symposion: dedicated to Kurt Schütte on the occasion of his 65th birthday: proceedings of the International Summer Institute and Logic Colloquium, Kiel, 1974.K. Schütte, Justus Diller & G. H. Müller (eds.) - 1975 - New York: Springer Verlag.