Sato, Kentaro (2015). Full and hat inductive definitions are equivalent in NBG. Archive for Mathematical Logic, 54(12), pp. 75112. Springer 10.1007/s001530140403x
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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 + 3th order number theory extending the socalled Bernays−Gödel expansion of full n + 2order number theory etc.) are. In this article, we establish the equivalence between Δ10\bfLFP and Δ10\bfFP, which assert the existence of a least and of a (not necessarily least) fixed point, respectively, for positive elementary operators (or between Δn+20\bfLFP and Δn+20\bfFP). 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 + 2th order number theory with global wellordering).
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:  09335846 
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/s001530140403x 
BORIS DOI:  10.7892/boris.61786 
URI:  http://boris.unibe.ch/id/eprint/61786 