Archive for Mathematical Logic

, Volume 53, Issue 7–8, pp 779–808 | Cite as

Admissibility and refutation: some characterisations of intermediate logics

  • Jeroen P. Goudsmit


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 in terms of their admissible rules. To illustrate the technique, we also provide a refutation system for Medvedev’s logic.


Intermediate logic Admissible rules Refutation Gabbay–de Jongh logics Medvedev’s logic 

Mathematics Subject Classification

03B20 03B55 


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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Utrecht UniversityUtrechtThe Netherlands

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