Bi-embeddability spectra and bases of spectra

Ekaterina Fokina; Dino Rossegger; Luca San Mauro

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arXiv · 1808.05451

Bi-embeddability spectra and bases of spectra

Ekaterina Fokina·Dino Rossegger·Luca San Mauro

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Abstract

We study degree spectra of structures with respect to the bi-embeddability relation. The bi-embeddability spectrum of a structure is the family of Turing degrees of its bi-embeddable copies. To facilitate our study we introduce the notions of bi-embeddable triviality and basis of a spectrum. Using bi-embeddable triviality we show that several known families of degrees are bi-embeddability spectra of structures. We then characterize the bi-embeddability spectra of linear orderings and study bases of bi-embeddability spectra of strongly locally finite graphs.

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Ekaterina Fokina, Dino Rossegger, Luca San Mauro. 2018-08-16. Bi-embeddability spectra and bases of spectra. https://arxiv.org/abs/1808.05451

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