Sato, Kentaro (2014). Relative Predicativity and dependent recursion in secondorder set theory and higherorders theories. The Journal of Symbolic Logic, 79(03), pp. 712732. 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+3th order number or set theories, where the class of all n+2th 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:  00224812 
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 