Monotone Inductive Definitions in Explicit Mathematics

@article{Rathjen1996MonotoneID,
  title={Monotone Inductive Definitions in Explicit Mathematics},
  author={Michael Rathjen},
  journal={J. Symb. Log.},
  year={1996},
  volume={61},
  pages={125-146}
}
The context for this paper is Feferman's theory of explicit mathematics, T 0 . We address a problem that was posed in [6]. Let MID be the principle stating that any monotone operation on classifications has a least fixed point. The main objective of this paper is to show that T 0 + MID , when based on classical logic, also proves the existence of non-monotone inductive definitions that arise from arbitrary extensional operations on classifications. From the latter we deduce that MID , when… CONTINUE READING