Addendum to ``Countable algebra and set existence axioms'' (Q1063594)

The authors admit that (one direction of) the proof of Theorem 3.1 of the above paper (see Zbl 0575.03038) is flawed; they retract the remark following that proof, which was based on the flawed part; and they provide an alternate proof of the theorem, strengthening it at the same time by adding to the two equivalent conditions a third one: (3) Every countable commutative ring with a unit has a radical ideal. Finally they fill the two question marks on top of page 148 by results from the literature.