Dick Jongh [5]Dick H. J. Jongh [2]Dick De Jongh [1]
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  1.  50
    On the proof of Solovay's theorem.Dick Jongh, Marc Jumelet & Franco Montagna - 1991 - Studia Logica 50 (1):51 - 69.
    Solovay's 1976 completeness result for modal provability logic employs the recursion theorem in its proof. It is shown that the uses of the recursion theorem can in this proof be replaced by the diagonalization lemma for arithmetic and that, in effect, the proof neatly fits the framework of another, enriched, system of modal logic (the so-called Rosser logic of Gauspari-Solovay, 1979) so that any arithmetical system for which this logic is sound is strong enough to carry out the proof, in (...)
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  2.  37
    Explicit fixed points in interpretability logic.Dick Jongh & Albert Visser - 1991 - Studia Logica 50 (1):39 - 49.
    The problem of Uniqueness and Explicit Definability of Fixed Points for Interpretability Logic is considered. It turns out that Uniqueness is an immediate corollary of a theorem of Smoryski.
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  3.  8
    Intermediate Logics and the de Jongh property.Dick Jongh, Rineke Verbrugge & Albert Visser - 2011 - Archive for Mathematical Logic 50 (1-2):197-213.
    We prove that all extensions of Heyting Arithmetic with a logic that has the finite frame property possess the de Jongh property.
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  4.  32
    A simplification of a completeness proof of Guaspari and Solovay.Dick H. J. Jongh - 1987 - Studia Logica 46 (2):187 - 192.
    The modal completeness proofs of Guaspari and Solovay (1979) for their systems R and R – are improved and the relationship between R and R – is clarified.
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  5.  15
    Extendible Formulas in Two Variables in Intuitionistic Logic.Nick Bezhanishvili & Dick Jongh - 2012 - Studia Logica 100 (1-2):61-89.
    We give alternative characterizations of exact, extendible and projective formulas in intuitionistic propositional calculus IPC in terms of n -universal models. From these characterizations we derive a new syntactic description of all extendible formulas of IPC in two variables. For the formulas in two variables we also give an alternative proof of Ghilardi’s theorem that every extendible formula is projective.
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    Generic generalized Rosser fixed points.Dick H. J. Jongh & Franco Montagna - 1987 - Studia Logica 46 (2):193 - 203.
    To the standard propositional modal system of provability logic constants are added to account for the arithmetical fixed points introduced by Bernardi-Montagna in [5]. With that interpretation in mind, a system LR of modal propositional logic is axiomatized, a modal completeness theorem is established for LR and, after that, a uniform arithmetical (Solovay-type) completeness theorem with respect to PA is obtained for LR.
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  7.  21
    Rosser orderings and free variables.Dick Jongh & Franco Montagna - 1991 - Studia Logica 50 (1):71 - 80.
    It is shown that for arithmetical interpretations that may include free variables it is not the Guaspari-Solovay system R that is arithmetically complete, but their system R –. This result is then applied to obtain the nonvalidity of some rules under arithmetical interpretations including free variables, and to show that some principles concerning Rosser orderings with free variables cannot be decided, even if one restricts oneself to usual proof predicates.
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