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 κ → σ n (κ) 2 .
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