English

Linearization of analytic order relations

Logic 2018-08-22 v1

Abstract

We prove that if \leq is an analytic partial order then either \leq can be extended to a (boldface) Δ21\Delta^1_2 linear order similar to an antichain in 2<ω12^{<\omega_1} ordered lexicographically or a certain Borel partial order 0\leq_0 embeds in .\leq. Some corollaries for analytic equivalence relations are given, for instance, if EE is a Σ11[z]\Sigma^1_1[z] equivalence relation such that E0E_0 does not embed in EE then EE is determined by intersections with E-invariand Borel sets coded in L[z]L[z].

Keywords

Cite

@article{arxiv.math/9706204,
  title  = {Linearization of analytic order relations},
  author = {Vladimir Kanovei},
  journal= {arXiv preprint arXiv:math/9706204},
  year   = {2018}
}