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  1. Decidability of admissibility: On a problem by Friedman and its solution by Rybakov.Jeroen P. Goudsmit - 2021 - Bulletin of Symbolic Logic 27 (1):1-38.
    Rybakov proved that the admissible rules of $\mathsf {IPC}$ are decidable. We give a proof of the same theorem, using the same core idea, but couched in the many notions that have been developed in the mean time. In particular, we illustrate how the argument can be interpreted as using refinements of the notions of exactness and extendibility.
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  • Admissibility and refutation: some characterisations of intermediate logics.Jeroen P. Goudsmit - 2014 - Archive for Mathematical Logic 53 (7-8):779-808.
    Refutation systems are formal systems for inferring the falsity of formulae. These systems can, in particular, be used to syntactically characterise logics. In this paper, we explore the close connection between refutation systems and admissible rules. We develop technical machinery to construct refutation systems, employing techniques from the study of admissible rules. Concretely, we provide a refutation system for the intermediate logics of bounded branching, known as the Gabbay–de Jongh logics. We show that this gives a characterisation of these logics (...)
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