Full and hat inductive definitions are equivalent in NBG

Sato, Kentaro (2015). Full and hat inductive definitions are equivalent in NBG. Archive for Mathematical Logic, 54(1-2), pp. 75-112. Springer 10.1007/s00153-014-0403-x

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A new research project has, quite recently, been launched to clarify how different, from systems in second order number theory extending ACA 0, those in second order set theory extending NBG (as well as those in n + 3-th order number theory extending the so-called Bernays−Gödel expansion of full n + 2-order number theory etc.) are. In this article, we establish the equivalence between Δ10\bf-LFP and Δ10\bf-FP, which assert the existence of a least and of a (not necessarily least) fixed point, respectively, for positive elementary operators (or between Δn+20\bf-LFP and Δn+20\bf-FP). Our proof also shows the equivalence between ID 1 and ^ID1, both of which are defined in the standard way but with the starting theory PA replaced by ZFC (or full n + 2-th order number theory with global well-ordering).

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: 0933-5846
Publisher: Springer
Language: English
Submitter: Florian Ranzi
Date Deposited: 23 Jan 2015 14:48
Last Modified: 02 Nov 2015 02:30
Publisher DOI: 10.1007/s00153-014-0403-x
BORIS DOI: 10.7892/boris.61786
URI: http://boris.unibe.ch/id/eprint/61786

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