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Ordinal definability and combinatorics of equivalence relations
Journal of Mathematical Logic ( IF 0.9 ) Pub Date : 2019-03-03 , DOI: 10.1142/s0219061319500090
William Chan 1
Affiliation  

Assume [Formula: see text]. Let [Formula: see text] be a [Formula: see text] equivalence relation coded in [Formula: see text]. [Formula: see text] has an ordinal definable equivalence class without any ordinal definable elements if and only if [Formula: see text] is unpinned.[Formula: see text] proves [Formula: see text]-class section uniformization when [Formula: see text] is a [Formula: see text] equivalence relation on [Formula: see text] which is pinned in every transitive model of [Formula: see text] containing the real which codes [Formula: see text]: Suppose [Formula: see text] is a relation on [Formula: see text] such that each section [Formula: see text] is an [Formula: see text]-class, then there is a function [Formula: see text] such that for all [Formula: see text], [Formula: see text].[Formula: see text] proves that [Formula: see text] is Jónsson whenever [Formula: see text] is an ordinal: For every function [Formula: see text], there is an [Formula: see text] with [Formula: see text] in bijection with [Formula: see text] and [Formula: see text].

中文翻译:

等价关系的序数可定义性和组合学

假设[公式:见正文]。令[Formula: see text] 为[Formula: see text] 中编码的[Formula: see text] 等价关系。[Formula: see text] 有一个没有任何序数可定义元素的序数可定义等价类当且仅当 [Formula: see text] 未固定。[Formula: see text] 证明 [Formula: see text] - 当 [Formula: : see text] 是 [Formula: see text] 上的 [Formula: see text] 等价关系,它固定在 [Formula: see text] 的每个传递模型中,其中包含实数 [Formula: see text]:假设 [Formula : see text] 是 [Formula: see text] 上的关系,使得每个部分 [Formula: see text] 是 [Formula: see text] 类,然后有一个函数 [Formula: see text] 使得对于所有[公式:见文],[公式:见文]。[公式:见文]证明[公式:
更新日期:2019-03-03
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