Abstract embeddability ranks
Metric Geometry
2023-05-24 v1 Functional Analysis
Logic
Abstract
We describe several ordinal indices that are capable of detecting, according to various metric notions of faithfulness, the embeddability between pairs of Polish spaces. These embeddability ranks are of theoretical interest but seem difficult to estimate in practice. Embeddability ranks, which are easier to estimate in practice, are embeddability ranks generated by Schauder bases. These embeddability are inspired by the nonlinear indices \`a la Bourgain from \cite{BLMS_FM}. In particular, we resolve a problem \cite[Problem 3.10]{BLMS_FM} regarding the necessity of additional set-theoretic axioms regarding the main coarse universality result of \cite{BLMS_FM}.
Cite
@article{arxiv.2305.13505,
title = {Abstract embeddability ranks},
author = {Florent P. Baudier and Christian Rosendal},
journal= {arXiv preprint arXiv:2305.13505},
year = {2023}
}
Comments
10 pages