A presentation of the initial lift-algebra

[摘要] 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) is an element of 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. (C) 1997 Elsevier Science B.V.

[发布日期] 1997-03-28