User blog comment:P進大好きbot/What does a computable large number mean?/@comment-4224897-20180610135217/@comment-27513631-20180613185452

Yeah. But your definition of 'reasonable' may happen to include \(\Sigma_1\)-sound, and we generally only really need one theory per language, as the language of the theory captures most (not all) of what we want the definition for.