A Minimal Degree Which Collapses $\omega_1$
Tim Carlson, Kenneth Kunen, Arnold W. Miller
Journal of Symbolic Logic, Vol. 49, No. 1. (Mar., 1984), pp. 298-300.
AbstractWe consider a well-known partial order of Prikry for producing a collapsing function of minimal degree. Assuming $MA + \neq CH$, every new real constructs the collapsing map.