  We study the effective versions of several notions related to incompleteness,
undecidability and inseparability along the lines of Pour-El's insights.
Firstly, we strengthen Pour-El's theorem on the equivalence between effective
essential incompleteness and effective inseparability. Secondly, we compare the
notions obtained by restricting that of effective essential incompleteness to
intensional finite extensions and extensional finite extensions. Finally, we
study the combination of effectiveness and hereditariness, and prove an adapted
version of Pour-El's result for this combination.
