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Jul 12, 2020 at 18:02 comment added Arno Yes, for those examples deciding the axioms is easy. Take for instance ZFC. There are finitely many special axioms, and then the axioms schema replacement and separation. Checking whether a given formula is an instace of the schema is just a pattern-matching issue.
Jul 12, 2020 at 17:52 comment added jg1896 Thank you very much. This is great. Since you pointed out, and I neglected, if we consider some canonical axiom system (ZFC, PA, Groups, modules, etc), the axioms can be decided polynomially, right?
Jul 12, 2020 at 17:49 vote accept jg1896
Jul 12, 2020 at 17:43 history answered Arno CC BY-SA 4.0