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Mar 4, 2014 at 21:00 comment added Lucas K. One way to prove that they are not necessary is to show that ZFC can prove the absolute consistency of such simplified system. Has such proof been given? I am not convinced that further simplifications are not possible.
Mar 3, 2014 at 0:26 comment added user5810 @LucasK. : $\:$ If you can't drop them, then they're not unnecessary. $\;\;\;\;$
Mar 2, 2014 at 21:37 comment added François G. Dorais @LucasK. Not really, see KP: en.wikipedia.org/wiki/Kripke%E2%80%93Platek_set_theory
Mar 2, 2014 at 21:18 comment added Lucas K. Those are the more obvious ones. But can you also drop unnecessary nesting of quantifyers?
Mar 2, 2014 at 21:15 history answered user44143 CC BY-SA 3.0