Math vs Logic

From the point of view of Mathematics, Russell's paradox has been
laid to rest through the Zermelo-Frankel Axioms(1920s) which constitute
the working  form of Set Theory. Below:

Number 7 prohibits X being an element of itself outright.


In 1960, the American mathematician Paul Cohen is deemed to have
shown that the axiom of choice is independent of the continuum hypothesis,
thus convincing the hold-outs that continuity and the axiom of choice are not linked.

From the point of view of Logic, Cohen's independence is in effect
undecidability.  An example of undecidability would  that parallel lines don't
meet with respect to Euclidian Geometry. One cannot decide whether this is
true or false from within Euclidian Geometry.