On Existentially Quantified Conjunctions of Atomic Formulae of L

Suucient conditions for an 9 , 89 , or 889 prenex L +-sentence to be translatable into the variable-free formalism L will be singled out in what follows. An eecient test based on such conditions will also be described. Through minor modiications of this testing algorithm, one can obtain the translation when the suucient conditions are met.