Fokina, E., Rossegger, D., & San Mauro, L. F. (2019). Bi‐embeddability spectra and bases of spectra. Mathematical Logic Quarterly, 65(2), 228–236. https://doi.org/10.1002/malq.201800056
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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