Geodesic
Computable embeddings for pairs of linear orders
Algebra i logika, Tome 60 (2021) no. 3, pp. 251-285

Voir la notice de l'article provenant de la source Math-Net.Ru

We study computable embeddings for pairs of structures, i.e., for classes containing precisely two nonisomorphic structures. Surprisingly, even for some pairs of simple linear orders, computable embeddings induce a nontrivial degree structure. Our main result shows that $\{\omega \cdot k,\omega^\star \cdot k\}$ is computably embeddable in $\{\omega \cdot t, \omega^\star \cdot t\}$ iff $k$ divides $t$.
Keywords: computable embedding, enumeration operator, computable linear order. 
@article{AL_2021_60_3_a0,
     author = {N. A. Bazhenov and H. Ganchev and S. Vatev},
     title = {Computable embeddings for pairs of linear orders},
     journal = {Algebra i logika},
     pages = {251--285},
     publisher = {mathdoc},
     volume = {60},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2021_60_3_a0/}
}
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N. A. Bazhenov; H. Ganchev; S. Vatev. Computable embeddings for pairs of linear orders. Algebra i logika, Tome 60 (2021) no. 3, pp. 251-285. http://geodesic.mathdoc.fr/item/AL_2021_60_3_a0/