Degree spectra of analytic complete equivalence relations
Logic
2023-10-19 v2
Abstract
We study the bi-embeddability and elementary bi-embeddability relation on graphs under Borel reducibility and investigate the degree spectra realized by this relations. We first give a Borel reduction from embeddability on graphs to elementary embeddability on graphs. As a consequence we obtain that elementary bi-embeddability on graphs is a analytic complete equivalence relation. We then investigate the algorithmic properties of this reduction to show that every bi-embeddability spectrum of a graph is the jump spectrum of an elementary bi-embeddability spectrum of a graph.
Keywords
Cite
@article{arxiv.2010.00755,
title = {Degree spectra of analytic complete equivalence relations},
author = {Dino Rossegger},
journal= {arXiv preprint arXiv:2010.00755},
year = {2023}
}