Journal article:

Samuel R. Buss.
"The modal logic of pure provability."
Notre Dame Journal of Formal Logic 31 (1990) 225-231.

Abstract: We introduce a propositional modal logic~$\PP$ of "pure" provability in arbitrary theories (propositional or first-order) where the $\nec$ operator means {\em "provable in all extensions"}. This modal logic has been considered in another guise by Kripke. An axiomatization and a decision procedure are given and the $\nec\poss$~subtheory is characterized.