Title: Degrees of Presentability of Structures. II
Abstract: We show that the property of being locally
constructivizable is inherited under Muchnik reducibility, which is
weakest among the effective reducibilities considered over
countable structures. It is stated that local constructivizability
of level higher than $1$ is inherited under $\Sigma$-reducibility but
is not inherited under Medvedev reducibility. An example of a
structure ${\mathfrak M}$ and a relation $P\subseteq M$ is
constructed for which $\underline{({\mathfrak M},P)}\equiv
\underline{{\mathfrak M}}$ but $({\mathfrak M},P)
\not\equiv_\Sigma{\mathfrak M}$. Also, we point out a class of
structures which are effectively defined by a family of their local
theories.
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