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arXiv · 2010.00755

Degree spectra of analytic complete equivalence relations

Dino Rossegger
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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.

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Dino Rossegger. 2020-10-02. Degree spectra of analytic complete equivalence relations. https://arxiv.org/abs/2010.00755

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