Linearization of definable order relations

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• 作者：Kanovei ; Vladimir
• 关键词：03E15 ; 03E35 ; 04A15 ; Linearization ; Partial order ; Souslin relation ; Solovay model
• 刊名：Annals of Pure and Applied Logic
• 出版年：2000
• 出版时间：March 3, 2000
• 年：2000
• 卷：102
• 期：1-2
• 页码：69-100
• 全文大小：264 K

文摘

We prove that if is an analytic partial order then either can be extended to a Δ₂¹ linear order similar to an antichain in 2^<ω₁, ordered lexicographically, or a certain Borel partial order ₀ embeds in . Similar linearization results are presented, for κ-bi-Souslin partial orders and real-ordinal definable orders in the Solovay model. A corollary for analytic equivalence relations says that any (lightface) Σ₁¹ equivalence relation such that does not embed in is fully determined by intersections with -invariant Borel sets coded in L.