Semiconvection and Overshooting: Schwarzschild and Ledoux Criteria Revisited

We show that the Schwarzschild formalism, if accepted as the description of the structure of a semiconvective region, necessarily implies overshooting. The Ledoux formalism (if accepted) can be used without overshooting, provided a new relation for the mixing-length parameter alpha is satisfied. Should the latter not be satisfied, the Ledoux formalism would also require overshooting, that is, a nonlocal convection model.