From hierarchies to well-foundedness

Flumini, Dandolo; Sato, Kentaro

doi:10.21256/zhaw-4782

Please use this identifier to cite or link to this item: https://doi.org/10.21256/zhaw-4782

Publication type:	Article in scientific journal
Type of review:	Peer review (publication)
Title:	From hierarchies to well-foundedness
Authors:	Flumini, Dandolo Sato, Kentaro
DOI:	10.21256/zhaw-4782 10.1007/s00153-014-0392-9
Published in:	Archive for Mathematical Logic
Volume(Issue):	53
Issue:	7-8
Page(s):	855
Pages to:	863
Issue Date:	2014
Publisher / Ed. Institution:	Springer
ISSN:	0933-5846 1432-0665
Language:	English
Subjects:	Transfinite recursion; Well-foundedness; Second order arithmetic; Second order set theory; pseudohierarchy; Intuitionistic logic
Subject (DDC):	510: Mathematics
Abstract:	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.
Further description:	Erworben im Rahmen der Schweizer Nationallizenzen (http://www.nationallizenzen.ch)
URI:	https://digitalcollection.zhaw.ch/handle/11475/15846
Fulltext version:	Published version
License (according to publishing contract):	Licence according to publishing contract
Departement:	School of Engineering
Organisational Unit:	Institute of Applied Mathematics and Physics (IAMP)
Appears in collections:	Publikationen School of Engineering

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Flumini, D., & Sato, K. (2014). From hierarchies to well-foundedness. Archive for Mathematical Logic, 53(7-8), 855–863. https://doi.org/10.21256/zhaw-4782

Flumini, D. and Sato, K. (2014) ‘From hierarchies to well-foundedness’, Archive for Mathematical Logic, 53(7-8), pp. 855–863. Available at: https://doi.org/10.21256/zhaw-4782.

D. Flumini and K. Sato, “From hierarchies to well-foundedness,” Archive for Mathematical Logic, vol. 53, no. 7-8, pp. 855–863, 2014, doi: 10.21256/zhaw-4782.

FLUMINI, Dandolo und Kentaro SATO, 2014. From hierarchies to well-foundedness. Archive for Mathematical Logic. 2014. Bd. 53, Nr. 7-8, S. 855–863. DOI 10.21256/zhaw-4782

Flumini, Dandolo, and Kentaro Sato. 2014. “From Hierarchies to Well-Foundedness.” Archive for Mathematical Logic 53 (7-8): 855–63. https://doi.org/10.21256/zhaw-4782.

Flumini, Dandolo, and Kentaro Sato. “From Hierarchies to Well-Foundedness.” Archive for Mathematical Logic, vol. 53, no. 7-8, 2014, pp. 855–63, https://doi.org/10.21256/zhaw-4782.