On the intermediate logic of open subsets of metric spaces

In this paper we study the intermediate logic MLO(X) of open subsets of a metric space X. This logic is closely related to Medvedev's logic of finite problems ML. We prove several facts about this logic: its inclusion in ML, impossibility of its finite axiomatization and indistinguishability from ML within some large class of propositional formulas.

• Type: Conference
• Year: 2008
• Where: AIML
• Authors: Timofei Shatrov
• Keywords: AIML 2008, Intermediate Logic, Logic, Logical Reasoning, Metric Space X