That is, we can quantify over non-existent things using the particular quantifier (also known misleadingly in the view of noneists as the existential quantifier).
These can be assigned values or can be quantified as to when they apply with the universal quantifier (always apply) or the existential quantifier (applies at least once).
The axioms below are grouped by the types of relation they invoke, then sorted, first by the number of existential quantifiers, then by the number of atomic sentences.
This definition, while terse and commonly used, is suboptimal for certain purposes because it contains an existential quantifier which is not really necessary.