Learn More
After a summary of earlier work it is shown that elementary or Kalmar arithmetic can be interpreted within the system of Russell's Principia Mathematica with the axiom of infinity but without the axiom of reducibility. 1 Historical introduction After discovering the inconsistency in Frege's Grundge-setze der Arithmetik, Russell proposed two changes: first,(More)
We show that the actuality operator A is redundant in any propositional modal logic characterized by a class of Kripke models (respectively, neighborhood models). Specifically, we prove that for every formula φ in the propositional modal language with A, there is a formula ψ not containing A such that φ and ψ are materially equivalent at the actual world in(More)