  In the field-antifield formalism, we review existence and uniqueness proofs
for the proper action in the reducible case. We give two new existence proofs
based on two resolution degrees called "reduced antifield number" and "shifted
antifield number", respectively. In particular, we show that for every choice
of gauge generators and their higher stage counterparts, there exists a proper
action that implements them at the quadratic order in the auxiliary variables.
