A presentation of the initial lift-algebra Original Research Article

The object of study of the present paper may be considered as a model, in an elementary topos with a natural numbers object, of a non-classical variation of the Peano arithmetic. The new feature consists in admitting, in addition to the constant (zero) s0 ε N and the unary operation (the successor map) s1 : N → N, arbitrary operations su : Nu → N of arities u ‘between 0 and 1’. That is, u is allowed to range over subsets of a singleton set.