Reflection and partition properties of admissible ordinals

Abstract

The present paper studies the relation between admissibility, reflection and partition properties. After introducing basic notions in Section e, Σ_n admissible ordinals are characterized using reflection properties (Section 2). Σ_n partition relations are introduced in Section 3. In Sections 3 and 4 connections are explored between partition properties, admissibility and projecta. Several more characterizations of admissibility are given in Section 5 (using Σ_n trees) and Section 6 (using Σ_n compactness). The ideas developed in Section 5 are used in Section 7 to study the partition relation .