During recent years there has been growing interest in logical calculi with infinitely long expressions (see e.g. [2; 4; 5]). However, all results obtained so far, many of them very remarkable, are semantic in character. The reason is that, while the syntax of the "classical" calculi could be "Gödelized" and then studied with the aid of the theory of recursive functions, no such procedure has so far been devised for the infinitistic calculi. To do this, one should possess transfinite analogues of the theory of recursive functions and of arithmetization.In the investigations reported here, such analogues are constructed and applied to infinitistic calculi.Let (*) a be an arbitrary, but fixed, regular initial ordinal. By ordinals we shall mean ordinals a , a function letter (f.l.) "ƒ*" for each £
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.