Embeddings of P(ω)/\rm Fin into Borel Equivalence Relations between ℓ_p and ℓ_q

2013/10/18 by Zhi Yin, Yin, Zhi
Mathematics · #2010: Primary 03E15 #Advanced Algebra and Geometry #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #FOS: Mathematics #Functional Analysis (math.FA) #Logic (math.LO) #Secondary 46B45 #math.FA #math.LO #msc:03E15 #msc:46B45

paper · pdf · doi:10.48550/arxiv.1310.4892

21 pages

arxiv created 2013/10/18 · openalex publication_date 2013/10/18 · arxiv updated 2013/10/21 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

We prove that, for 1 ≤ p<q<∞, the partially ordered set P(ω)/\rm Fin can be embedded into Borel equivalence relations between ℝ^ω/ℓ_p and ℝ^ω/ℓ_q. Since there is an antichain of size continuum in P(ω)/\rm Fin, therefore there are continuum many incomparable Borel equivalence relations between ℝ^ω/ℓ_p and ℝ^ω/ℓ_q.

Related

• Borel equivalence relations between ℓ₁ and ℓ_p
• On ℓ^p-like equivalence relations
• Canonical equivalence relations on fronts on FIN_k
• Characterization of ℓ_p-like and c₀-like equivalence relations
• The Effective Theory of Borel Equivalence Relations