Geodesic
Spectra of degrees of some structures
Algebra i logika, Tome 46 (2007) no. 6, pp. 729-744

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We argue for the existence of structures with the spectrum $\{\mathbf x:\mathbf x\not\le\mathbf a\}$ of degrees, where $\mathbf a$ is an arbitrary low degree. Also it is stated that there exist structures with the spectrum of degrees, $\{\mathbf x:\mathbf x\not\le\mathbf a\}\cup\{\mathbf x:\mathbf x\not\le\mathbf b\}$, for any low degrees $\mathbf a$ and $\mathbf b$.
Keywords: degrees of unsolvability, relative enumerability, presentations of structures, computable structures. 
@article{AL_2007_46_6_a3,
     author = {I. Sh. Kalimullin},
     title = {Spectra of degrees of some structures},
     journal = {Algebra i logika},
     pages = {729--744},
     publisher = {mathdoc},
     volume = {46},
     number = {6},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2007_46_6_a3/}
}
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I. Sh. Kalimullin. Spectra of degrees of some structures. Algebra i logika, Tome 46 (2007) no. 6, pp. 729-744. http://geodesic.mathdoc.fr/item/AL_2007_46_6_a3/