Proof Theory for Intuitionistic Stable Theories

In this paper we show how to extend the standard cut-elimination procedure from first-order intuitionistic stable logic to a class of intuitionistic stable theories. Building on previous works by Negri and von Plato, we aptly modify the underlying calculus for first-order intuitionistic logic so as to preserve the admissibility of all the structural rules, including cut, in the presence of a restricted version of the rule of classical reductio ad absurdum and of a special case of universal rules.