Abstract

Roughly speaking, a pattern is a finite sequence coding the set of natural numbers n for which the Σ n + 1 projectum is less than the Σ n projectum for a given admissible ordinal. We prove that for each pattern there exists an ordinal realizing it. Several results on the orderings of patterns are given. We conclude the paper with remarks on ▵ n projecta. The main technique, used throughout the paper, is Jensen's Uniformisation Theorem