EDIT: On François' advice, I am adding here some clarifications which appear in comments.
Full comprehension is used.
Successoring is considered to be a 2-ary relationship, addition and multiplication to be 3-ary relationships. The usual axioms can be easily restated in these terms.
The logic is supposed to include variable n-ary relationships, for n = 1 but also for n > 1, which can be quantified over and whose existence can be proved using comprehension. So for instance, FPA is able to define size equivalence in the straightfoward fashion: A ~ B if and only if (there exists R)(R is a 1-1 function from A onto B). (In fact, given this apparatus, addition and multiplication can be defined from successoring, so one doesn't even need axioms about addition and multiplication, although this is a detail which should not affect the question asked.)
Induction can be considered to be:(P)(P0 & (n)(m)(Pn & Nn & Sn,m => Pm) => (n)(Nn => Pn)),where "N" is "is natural number" and "S" is successoring.
There are many ways to assert the infinity of primes. One way would be to define "a < b" as
(there exists x)(x > 0 & +(a,x,b)) and
"MP,n" (P has size n) as
P ~ {x : x < n}. Then
(not there exists n)(Nn & M{p : p is prime},n)
asserts the infinity of primes. Or one can state in via unboundedness: (n)(Nn => (there exists p)(p > n and p is prime)).
