Relative Predicativity and dependent recursion in second-order set theory and higher-orders theories
Publisher DOI
Abstract
This article reports that some robustness of the notions of predicativity and of autonomous progression is broken down if as the given infinite total entity we choose some mathematical entities other than the traditional ω. Namely, the equivalence between normal transfinite recursion scheme and new dependent transfinite recursion scheme, which does hold in the context of subsystems of second order number theory, does not hold in the context of subsystems of second order set theory where the universe V of sets is treated as the given totality (nor in the contexts of those of n+3-th order number or set theories, where the class of all n+2-th order objects is treated as the given totality).
Date Issued
2014
Publication Type
Article
Language(s)
en
Additional Credits
Journal
The journal of symbolic logic
Publisher
Cambridge University Press
ISSN
0022-4812
Access(Rights)
open.access