Аннотация
We investigate the complexity of embeddings between bi-embeddable structures. In analogy with categoricity spectra, we define the bi-embeddable categoricity spectrum of a structure A as the family of Turing degrees that compute embeddings between any computable bi-embeddable copies of A; the degree of bi-embeddable categoricity of A is the least degree in this spectrum (if it exists). We extend many known results about categoricity spectra to the case of bi-embeddability. In particular, we exhibit structures without degree of bi-embeddable categoricity, and we show that every degree d.c.e above 0 ( α ) for α a computable successor ordinal and 0 ( λ ) for λ a computable limit ordinal is a degree of bi-embeddable categoricity. We also give examples of families of degrees that are not bi-embeddable categoricity spectra.
Язык оригинала | английский |
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Страницы (с-по) | 1-16 |
Число страниц | 16 |
Журнал | Computability |
Том | 10 |
Номер выпуска | 1 |
DOI | |
Состояние | Опубликовано - 2021 |