Please use this identifier to cite or link to this item: https://doi.org/10.21256/zhaw-4782
Title: From hierarchies to well-foundedness
Authors : Flumini, Dandolo
Sato, Kentaro
Published in : Archive for mathematical logic
Volume(Issue) : 53
Issue : 7-8
Pages : 855
Pages to: 863
Publisher / Ed. Institution : Springer
Issue Date: 2014
License (according to publishing contract) : Licence according to publishing contract
Type of review: Peer review (Publication)
Language : English
Subjects : Transfinite recursion; Well-foundedness; Second order arithmetic; Second order set theory; pseudohierarchy; Intuitionistic logic
Subject (DDC) : 500: Natural sciences and 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)
Departement: School of Engineering
Organisational Unit: Institute of Applied Mathematics and Physics (IAMP)
Publication type: Article in scientific Journal
DOI : 10.21256/zhaw-4782
10.1007/s00153-014-0392-9
ISSN: 0933-5846
1432-0665
URI: https://digitalcollection.zhaw.ch/handle/11475/15846
Appears in Collections:Publikationen School of Engineering

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