Consider ZFC with both Powerset and Infinity removed and Collection included. The Well-Ordering Principle is not assumed.
Does this theory prove that, for every set $X$, there is a set of all finite subsets of $X$?
Consider ZFC with both Powerset and Infinity removed and Collection included. The Well-Ordering Principle is not assumed.
Does this theory prove that, for every set $X$, there is a set of all finite subsets of $X$?