Degree spectra of relations on structures of finite computable dimension (Q1612487)

The author proves that for every c.e. (\(\alpha\)-c.e., \(\alpha\in\omega\cup\{\omega\}\)) degree \(\mathbf d>0\) there is a computable structure whose algorithmic dimension is 2 and an intrinsically c.e. (\(\alpha\)-c.e.) relation on it such that its degree spectrum is \textbf{\{0,d\}}. Some generalizations and variations of this result are also considered.