Geodesic
The degree of decidable categoricity of a model with infinite solutions for complete formulas
Algebra i logika, Tome 60 (2021) no. 3, pp. 303-312

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We construct a decidable prime model in which the degree of a set of complete formulas is equal to $\mathbf{0}'$, infinitely many tuples of elements comply with every complete formula, and the decidable categoricity spectrum coincides with the set of all $PA$-degrees.
Keywords: computable model, decidable model, computable categoricity, autostability relative to strong constructivizations, degree of decidable categoricity, decidable categoricity spectrum, $PA$-degree. 
@article{AL_2021_60_3_a3,
     author = {S. S. Goncharov and M. I. Marchuk},
     title = {The degree of decidable categoricity of a model with infinite solutions for complete formulas},
     journal = {Algebra i logika},
     pages = {303--312},
     publisher = {mathdoc},
     volume = {60},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2021_60_3_a3/}
}
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S. S. Goncharov; M. I. Marchuk. The degree of decidable categoricity of a model with infinite solutions for complete formulas. Algebra i logika, Tome 60 (2021) no. 3, pp. 303-312. http://geodesic.mathdoc.fr/item/AL_2021_60_3_a3/