In Computer Science, n-tuples and lists are usual tools ; we investigate both notions in the framework of first-order logic within the set of nonnegative integers. Gödel had firstly shown that the objects which can be defined by primitive recursion schema, also can be defined at first-order, using natural order and some coding devices for lists. Secondly he had proved that this encoding can be defined from addition and multiplication. We show this can be also done with addition and a weaker… CONTINUE READING