Saved in:
Bibliographic Details
Main Author: Malicki, Maciej
Format: Preprint
Published: 2022
Subjects:
Online Access:https://arxiv.org/abs/2209.05903
Tags: Add Tag
No Tags, Be the first to tag this record!
Table of Contents:
  • We study the isomorphism relation on Borel classes of locally compact Polish metric structures. We prove that isomorphism on such classes is always classifiable by countable structures (equivalently: Borel reducible to graph isomorphism), which implies, in particular, that isometry of locally compact Polish metric spaces is Borel reducible to graph isomorphism. We show that potentially $\pmbΠ^0_{α+1}$ isomorphism relations are Borel reducible to equality on hereditarily countable sets of rank $α$, $α\geq 2$. We also study approximations of the Hjorth-isomorphism game, and formulate a condition ruling out classifiability by countable structures.