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.
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