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A note on iterative arguments in a topos. (English) Zbl 0767.18003
Least fixed points (say subalgebras spanned by subsets) may, in the topos of sets, be constructed from above (through a large intersection), or from below, by an iterative process (possibly transfinite). In any topos, the from-above procedure is well understood; the status of the from-below procedure is investigated in the present paper. The point is that no use is made of any natural number object, let alone ordinal number object, to parametrize the stages in the iteration.
The results are used by the author, in the context of general topology in a topos, in the paper reviewed below [see Zbl 0767.18004].
Reviewer: A.Kock (Aarhus)

MSC:
18B25 Topoi
03F50 Metamathematics of constructive systems
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