Abstract
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) s 0 ϵ N and the unary operation (the successor map) s 1 : N → N, arbitrary operations s u : N u → N of arities u ‘between 0 and 1’. That is, u is allowed to range over subsets of a singleton set.
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