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  1.  5
    Dick de Jongh, Marc Jumelet & Franco Montagna (1991). On the Proof of Solovay's Theorem. 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 replaced by the diagonalization lemma for arithmetic and that, in effect, the proof neatly fits the framework of another, enriched, system of modal logic so that any arithmetical system for which this logic is sound is strong enough to carry out the proof, in particular $\text{I}\Delta _{0}+\text{EXP}$ . The method is adapted (...)
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  2.  27
    Dick Jongh, Marc Jumelet & Franco Montagna (1991). On the Proof of Solovay's Theorem. 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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  3.  3
    Marc Jumelet (1995). Euler'sϕ-Function in the Context of IΔ 0. Archive for Mathematical Logic 34 (3):197-209.
    It is demonstrated that we can represent Euler's φ-function by means of a Δ0-formula in such a way that the theory IΔ 0 proves the recursion equations that are characteristic for this function.
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    Marc Jumelet (1995). Eulers [Mathematical Formula]-Function in the Context of [Mathematical Formula]. Archive for Mathematical Logic 3 (3):197-209.
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    Marc Jumelet (1995). Euler's $\Varphi$ -Function in the Context of ${\Rm I}\Delta_0$. Archive for Mathematical Logic 34 (3):197-209.
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