From hierarchies to well-foundedness

Flumini, Dandolo; Sato, Kentaro (2014). From hierarchies to well-foundedness. Archive for mathematical logic, 53(7-8), pp. 855-863. Springer International 10.1007/s00153-014-0392-9

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We highlight that the connection of well-foundedness and recursive definitions is more than just convenience. While the consequences of making well-foundedness a sufficient condition for the existence of hierarchies (of various complexity) have been extensively studied, we point out that (if parameters are allowed) well-foundedness is a necessary condition for the existence of hierarchies e.g. that even in an intuitionistic setting (Π01−CA0)α⊢wf(α)where(Π01−CA0)α stands for the iteration of Π01 comprehension (with parameters) along some ordinal α and wf(α) stands for the well-foundedness of α.

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:

Flumini, Dandolo, Sato, Kentaro

Subjects:

000 Computer science, knowledge & systems
500 Science > 510 Mathematics

ISSN:

0933-5846

Publisher:

Springer International

Language:

English

Submitter:

Florian Ranzi

Date Deposited:

23 Jan 2015 14:50

Last Modified:

05 Dec 2022 14:39

Publisher DOI:

10.1007/s00153-014-0392-9

BORIS DOI:

10.7892/boris.61787

URI:

https://boris.unibe.ch/id/eprint/61787

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