Quantifiers range over set and those are denoted by lower case letters. As is common in the study of set theory, one makes use set builder notation for classes, which, in most contexts, are not part of the object language but used for concise discussion. In particular, one may introduce notation declarations of the corresponding class via "formula_29", for the purpose of expressing formula_30 as formula_31. Logically equivalent predicates can be used to introduce the same class. One also writes formula_32 as shorthand for formula_33.