\(\Sigma_2\)-constructions and \(\text{I}\Sigma_1\) (Q1295390)

This paper establishes the provability in I\(\Sigma_1\) of the following embedding result: any recursive partial order with a maximal element can be embedded in the r.e. degrees with the maximal element mapping to any prescribed nonrecursive, incomplete degree. Consequently, statements of a certain form in the language of partial orders are eliminated as possible candidates for statements that can be proved by \(\Sigma_2\) priority arguments but cannot be proved in I\(\Sigma_1\).