可容许序数的反射和划分性质

Annals of Mathematical Logic Pub Date : 1982-08-01 DOI:10.1016/0003-4843(82)90022-5

Evangelos Kranakis

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引用次数: 13

摘要

本文研究了可容许性、反射性和分割性之间的关系。在第e节中介绍了基本概念之后，Σn可容许序数用反射性质来表征(第2节)。Σn分区关系在第3节中介绍。在第3节和第4节中，探讨了分区属性、可接受性和项目之间的联系。在第5节(使用Σn树)和第6节(使用Σn紧致性)中给出了更多的可采性特征。第5节中提出的思想在第7节中用于研究划分关系κ→σn (κ)2。

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Reflection and partition properties of admissible ordinals

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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Annals of Mathematical Logic

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