On spectrally universal classes of structures

For a countable algebraic structure $S$, the degree spectrum of $S$ is the set of Turing degrees of all isomorphic copies of $S$. A class of structures $K$ is spectrally universal if for every countable structure $S$, there exists a structure $M$ from $K$ such that the degree spectra of $M$ and $S$ are the same. The talk discusses recent results on spectral universality for some familiar algebraic classes: modal algebras, contact Boolean algebras, Heyting algebras with distinguished atoms and coatoms.
The work is supported by the Mathematical Center in Akademgorodok under the agreement No. 075-15-2022-281 with the Ministry of Science and Higher Education of the Russian Federation.