Archive for Mathematical Logic

, Volume 45, Issue 5, pp 581–599

On the rules of intermediate logics

Article

DOI: 10.1007/s00153-006-0320-8

Cite this article as:
Iemhoff, R. Arch. Math. Logic (2006) 45: 581. doi:10.1007/s00153-006-0320-8

Abstract

If the Visser rules are admissible for an intermediate logic, they form a basis for the admissible rules of the logic. How to characterize the admissible rules of intermediate logics for which not all of the Visser rules are admissible is not known. In this paper we give a brief overview of results on admissible rules in the context of intermediate logics. We apply these results to some well-known intermediate logics. We provide natural examples of logics for which the Visser rule are derivable, admissible but nonderivable, or not admissible.

Mathematics Subject Classification (2000)

03B2003F5003B5503F0303F55

Keywords or phrases

Intermediate logicsadmissible rulesrealizabilityRieger-Nishimura formulasMedvedev logicIndependence of Premise

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Institute for Discrete Mathematics and Geometry E104Vienna University of TechnologyViennaAustria