PP200006: Iemhoff, Rosalie (2000) A(nother) characterization of Intuitionistic Propositional Logic. [Report]
Text (Full Text)
PP200006.text.ps.gz Download (72kB) 

Text (Abstract)
PP200006.abstract.txt Download (1kB) 
Abstract
In \cite{iemhoff} we gave a countable basis $\cal V$ for the admissible rules of $\ipc$. Here we show that there is no proper superintuitionistic logic with the disjunction property for which all rules in $\cal V$ are admissible. This shows that, relative to the disjunction property, $\ipc$ is maximal with respect to its set of admissible rules. This characterization of $\ipc$ is optimal in the sense that no finite subset of $\cal V$ suffices. In fact, it is shown that for any finite subset $X$ of $\cal V$, for one of the proper superintuitionistic logics $D_n$ constructed by De Jongh and Gabbay (1974) all the rules in $X$ are admissible. Moreover, the logic $D_n$ in question is even characterized by $X$: it is the maximal superintuitionistic logic containing $D_n$ with the disjunction property for which all rules in $X$ are admissible. Finally, the characterization of $\ipc$ is proved to be effective by showing that it is effectively reducible to an effective characterization of $\ipc$ in terms of the Kleene slash by De Jongh (1970).
Item Type:  Report 

Report Nr:  PP200006 
Series Name:  Prepublication (PP) Series 
Year:  2000 
Date Deposited:  12 Oct 2016 14:36 
Last Modified:  12 Oct 2016 14:36 
URI:  https://eprints.illc.uva.nl/id/eprint/33 
Actions (login required)
View Item 