# Bi‐embeddability spectra and bases of spectra

@article{Fokina2018BiembeddabilitySA, title={Bi‐embeddability spectra and bases of spectra}, author={Ekaterina B. Fokina and Dino Rossegger and Luca San Mauro}, journal={Mathematical Logic Quarterly}, year={2018}, volume={65} }

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…

## 11 Citations

### DEGREE SPECTRA OF ANALYTIC COMPLETE EQUIVALENCE RELATIONS

- MathematicsThe Journal of Symbolic Logic
- 2021

Abstract We study the bi-embeddability and elementary bi-embeddability relation on graphs under Borel reducibility and investigate the degree spectra realized by these relations. We first give a…

### Elementary Bi-embeddability Spectra of Structures

- MathematicsCiE
- 2018

Primary bi-embeddability spectra, the collection of Turing degrees of elementary bi- embeddable structures, are studied and examples of such spectra are given.

### Degrees of bi-embeddable categoricity

- Mathematics, Computer ScienceComput.
- 2021

The bi-embeddable categoricity spectrum of a structure $\mathcal A$ is defined as the family of Turing degrees that compute embeddings between any computable bi- embeddable copies of $\math Cal A$; the degree of bi- embeddeddable categorics is the least degree in this spectrum (if it exists).

### On bi-embeddable categoricity of algebraic structures

- Mathematics, Computer ScienceAnn. Pure Appl. Log.
- 2022

### Computable Bi-Embeddable Categoricity

- MathematicsAlgebra and Logic
- 2018

We study the algorithmic complexity of isomorphic embeddings between computable structures. Suppose that L is a language. We say that L -structures A and B are bi-embeddable (denoted A ≈ B ) if there…

### Degrees of bi-embeddable categoricity of equivalence structures

- Mathematics, Computer ScienceArch. Math. Log.
- 2019

It is proved that computable equivalence structures have degree of bi-embeddable categoricity, and it is shown that the notions of $$Delta ^0_\alpha $$Δα0 bi- embeddableategoricity and relative $$ Delta ^0-\alpha$$ coincide for equivalence structure for $$alpha =1,2,3$$α=1, 2,3.

### Computable Reducibility for Computable Linear Orders of Type ω

- MathematicsJournal of Mathematical Sciences
- 2022

We study computable reducibility for computable isomorphic copies of the standard ordering of natural numbers. Following Andrews and Sorbi, we isolate the class of self-full degrees inside the…

### Degree Spectra of Structures Relative to Equivalences

- Materials ScienceAlgebra and Logic
- 2019

A standard way to capture the inherent complexity of the isomorphism type of a countable structure is to consider the set of all Turing degrees relative to which the given structure has a computable…

### Degrees of bi-embeddable categoricity of equivalence structures

- Materials ScienceArchive for Mathematical Logic
- 2018

We study the algorithmic complexity of embeddings between bi-embeddable equivalence structures. We define the notions of computable bi-embeddable categoricity, (relative)…

### Degree Spectra of Structures Relative to Equivalences

- Mathematics, Computer ScienceAlgebra i logika
- 2019

The degree spectrum of a theory is generalized to arbitrary equivalence relations iff the Σn theories of A and B coincide and study degree spectra with respect to ≡∑n$$ {\equiv}_{\sum_n} $$.

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Primary bi-embeddability spectra, the collection of Turing degrees of elementary bi- embeddable structures, are studied and examples of such spectra are given.

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We study the algorithmic complexity of isomorphic embeddings between computable structures. Suppose that L is a language. We say that L -structures A and B are bi-embeddable (denoted A ≈ B ) if there…

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It is proved that computable equivalence structures have degree of bi-embeddable categoricity, and it is shown that the notions of $$Delta ^0_\alpha $$Δα0 bi- embeddableategoricity and relative $$ Delta ^0-\alpha$$ coincide for equivalence structure for $$alpha =1,2,3$$α=1, 2,3.

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