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.
Fokina, E., Rossegger, D., San Mauro, L. (2019). Bi-embeddability spectra and bases of spectra. MATHEMATICAL LOGIC QUARTERLY, 65(2), 228-236 [10.1002/malq.201800056].
Bi-embeddability spectra and bases of spectra
San Mauro L.
2019-01-01
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.File | Dimensione | Formato | |
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https://hdl.handle.net/11365/1116006