I don't know who Peter Singer is. "Post-birth abortion" is an example of a ridiculous term. Abortion, by definition, can only occur before birth. Even the partial-birth abortion term is ridiculous, it has to be one or the other.
Also, if abortion is murder, then all parties should be prosecuted, the woman, the doctor, and any legislator who supports it. Not likely that will happen.
Post-birth abortion is not a ridiculous term. It happens in the state of Illinois and is protected by law. When the Illinois legislature considered a statute forcing the care of the born-alive baby following an unsuccessful abortion attempt, none other than ‘rat candidate Barack Hussein Obama voted against it. To this day standard procedure in Illinois is to place the live baby on a shelf and wait for it to die.