ON EXTENSIONS OF EMBEDDINGS INTO THE ENUMERATION DEGREES OF THE ${\Sigma_2^0}$-SETS.

We give an algorithm for deciding whether an embedding of a finite partial order ${\mathcal P}$ into the enumeration degrees of the ${\Sigma_2^0}$-sets can always be extended to an embedding of a finite partial order ${\mathcal Q} \supset {\mathcal P}$. [ABSTRACT FROM AUTHOR]