Bazhenov, N., Benavente-Fokina, E., Rossegger, D., & San Mauro, L. F. (2019). Degrees of bi-embeddable categoricity of equivalence structures. Archive for Mathematical Logic, 58, 543–563. https://doi.org/10.1007/s00153-018-0650-3
Computable categoricity; Bi-embeddability; degrees of categoricity; Degrees of bi-embeddable categoricity
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Abstract:
We study the algorithmic complexity of embeddings between bi-embeddable equivalence structures. We define the notions of computable bi-embeddable categoricity, (relative) Δ⁰α bi-embeddable categoricity, and degrees of bi-embeddable categoricity. These notions mirror the classical notions used to study the complexity of isomorphisms between structures. We show that the notions of Δ⁰α bi-embeddable categoricity and relative Δ⁰α bi-embeddable categoricity coincide for equivalence structures for α = 1, 2, 3. We also prove that computable equivalence structures have degree of bi-embeddable categoricity 0, 0', or 0''. We furthermore obtain results on the index set complexity of computable equivalence structure with respect to bi-embeddability.
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außerhalb der gesamtuniversitären Forschungsschwerpunkte: 100%
