Linearization of definable order relations

Annals of Pure and Applied Logic 102 (1-2):69-100 (2000)

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Abstract
We prove that if ≼ is an analytic partial order then either ≼ can be extended to a Δ 2 1 linear order similar to an antichain in 2 ω 1 , 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 Σ 1 1 equivalence relation E , such that E 0 does not embed in E , is fully determined by intersections with E -invariant Borel sets coded in L
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DOI 10.1016/s0168-0072(99)00013-5
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References found in this work BETA

Thin Equivalence Relations and Effective Decompositions.Greg Hjorth - 1993 - Journal of Symbolic Logic 58 (4):1153-1164.
Two Results on Borel Orders.Alain Louveau - 1989 - Journal of Symbolic Logic 54 (3):865-874.

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Citations of this work BETA

Glimm-Effros for Coanalytic Equivalence Relations.Greg Hjorth - 2009 - Journal of Symbolic Logic 74 (2):402-422.

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