3 years ago

Bi-embeddability spectra and bases of spectra.

Ekaterina Fokina, Dino Rossegger, Luca San Mauro

We study degree spectra of structures relative to the bi-embeddability relation. The bi-embeddability spectrum of a structure is the family of Turing degrees of structures bi-embeddable with it. We introduce the notions of bi-embeddable triviality and basis of a spectrum. Using bi-embeddable triviality we show that several well known classes of degrees are bi-embeddability spectra of structures. We then give a complete characterization of bi-embeddability spectra of linear orderings and investigate bases of bi-embeddability spectra of strongly locally finite graphs. We show that there is a strongly locally finite graph without finite bi-embeddability basis.

Publisher URL: http://arxiv.org/abs/1808.05451

DOI: arXiv:1808.05451v1

You might also like
Discover & Discuss Important Research

Keeping up-to-date with research can feel impossible, with papers being published faster than you'll ever be able to read them. That's where Researcher comes in: we're simplifying discovery and making important discussions happen. With over 19,000 sources, including peer-reviewed journals, preprints, blogs, universities, podcasts and Live events across 10 research areas, you'll never miss what's important to you. It's like social media, but better. Oh, and we should mention - it's free.

  • Download from Google Play
  • Download from App Store
  • Download from AppInChina

Researcher displays publicly available abstracts and doesn’t host any full article content. If the content is open access, we will direct clicks from the abstracts to the publisher website and display the PDF copy on our platform. Clicks to view the full text will be directed to the publisher website, where only users with subscriptions or access through their institution are able to view the full article.