Archive for Mathematical Logic

, Volume 53, Issue 7–8, pp 779–808

# Admissibility and refutation: some characterisations of intermediate logics

Article

## Abstract

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.

### Keywords

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

03B20 03B55

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© Springer-Verlag Berlin Heidelberg 2014

## Authors and Affiliations

1. 1.Utrecht UniversityUtrechtThe Netherlands