Bi-embeddability spectra and basis of spectra

Mathematical Logic Quarterly 2 (65):228-236 (2019)
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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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Luca San Mauro
Università degli Studi di Roma La Sapienza

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