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A note on iterative arguments in a topos

Published online by Cambridge University Press:  24 October 2008

J. J. C. Vermeulen
J. J. C. Vermeulen
Affiliation:
Department of Mathematics, University of Cape Town, Rondebosch 7700, South Africa
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Extract

Intuitively, transfinite iteration is a repetitive process, which eventually reaches completion, but might need to progress through an infinite chain of steps before finally doing so. But whereas such a chain is always readily at hand in classical set theory in the form of ordinals, iterative arguments involving sets (i.e. objects) in a general topos have to depend on some intrinsic or naturally available inductive structure, say algebraic, which might not be associated with a (well-ordered) chain.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 111 , Issue 1 , January 1992 , pp. 57 - 62
Copyright
Copyright © Cambridge Philosophical Society 1992

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References

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