Relative Predicativity and dependent recursion in second-order set theory and higher-orders theories

Sato, Kentaro (2014). Relative Predicativity and dependent recursion in second-order set theory and higher-orders theories. The Journal of Symbolic Logic, 79(03), pp. 712-732. 10.1017/jsl.2014.28

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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).

Item Type: Journal Article (Original Article)
Division/Institute: 08 Faculty of Science > Institute of Computer Science (INF) > Logic and Theory Group (LTG)
08 Faculty of Science > Institute of Computer Science (INF)
UniBE Contributor: Sato, Kentaro
Subjects: 000 Computer science, knowledge & systems
500 Science > 510 Mathematics
ISSN: 0022-4812
Language: English
Submitter: Florian Ranzi
Date Deposited: 23 Jan 2015 14:53
Last Modified: 23 Jan 2015 14:53
Publisher DOI: 10.1017/jsl.2014.28
BORIS DOI: 10.7892/boris.61784
URI: http://boris.unibe.ch/id/eprint/61784

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