ABSTRACT
D efinition 4.2. If M is an ^-structure, and (p(x\ , X2 , . . . , x*) is a formula of Ccou(0 with just finitely many free variables, then we can define
by induction on the complexity o f in the usual way. The only clauses which differ from first-order logic are the ones corresponding to infinite conjunction and disjunction, and here we stipulate that
and
(i) The infinite conjunction \ J ieN V i € £<^,0, and infinite disjunction A /gn V i ^ £ 0,1,0, depend solely on the set {y/t \ i e N}, and not the par ticular enumeration (y/i)ie ^.
