Borel equivalence relations between \ell_1 and \ell_p

TL;DR

This paper demonstrates the existence of a vast continuum of Borel equivalence relations between certain quotient spaces of  and _p, which are pairwise Borel incomparable, revealing complex structures in descriptive set theory.

Contribution

It establishes the existence of continuum many pairwise Borel incomparable equivalence relations between / and /_p for each p>1, expanding understanding of Borel reducibility.

Findings

Existence of continuum many such relations.

Relations are pairwise Borel incomparable.

Results apply for all p>1.

Abstract

In this paper, we show that, for each $p>1$, there are continuum many Borel equivalence relations between $\Bbb R^\omega/\ell_1$ and $\Bbb R^\omega/\ell_p$ ordered by $\le_B$ which are pairwise Borel incomparable.