Title: Degrees of Presentability of Structures. I
Abstract: Presentations of structures in admissible sets, as
well as different relations of effective reducibility between the
structures, are treated. Semilattices of degrees of $\Sigma$-definability
are the main object of investigation. It is shown that the
semilattice of degrees of $\Sigma$-definability of countable structures
agrees well with semilattices of $T$- and $e$-degrees of subsets of
natural numbers. Also an attempt is made to study properties
of the structures that are inherited under various effective
reducibilities and explore how degrees of presentability depend on
choices of different admissible sets as domains for
presentations.
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