What is a Primitive Atomic Formula? I am reading "Axiomatic Set Theory" by Patrick Suppes and he defines a primitive atomic formula as follows:
A primitive atomic is an expression of the form ($v\in w$ ), or of the form ($v=w$) where v and w are either general variables or constant '0'(empty set).
My question is what is a primitive atomic formula? Is it a statement of predicate logic that has a clear meaning that makes sense in the language? Come to think of it, if it doesn't take too long to explain whats a primitive formula?
 A: In a standard first-order language an atomic formula is just an $n$-place predicate (from the stock of $n$-place predicates in the language's basic vocabulary) followed by $n$ terms. A term is whatever you can form from the function-expressions, names and variables of the language in the usual way explained in any logic text.
The primitive language of axiomatic set theory (unaugmented by the introduction of additional defined expressions) is exceptionally sparse. There are at most two built-in predicates, '$\in$' and '$=$' (see Carl Mummert's comment). And since there are no constants in the language, and no buiit-in function expressions either (remember, we are talking about the initial unaugmented language), the only terms are variables. So the only atomic formulae are the likes of '$\in vw$' and  '$= vw$', conventionally re-written  '$v \in w$' and  '$v=w$'. 
Finally, talk of primitive atomic formulae here just highlights that we are talking of atomic formulae of the basic, unaugmented, primitive (call it what you will) language.
