Systems of predicative analysis, II: Representations of ordinals

Abstract

The eventual purpose of this paper is to provide certain specific representations of ordinals and develop their basic properties as needed for the proofs of the results announced in [3]. Since the choice of these representations is really intelligible only if the general principles involved are made explicit, we devote the first half of this paper (§§1 and 2) to such questions. The entire treatment is self-contained.