Rathjen, M, Van Der Meeren, J and Weiermann, A (2017) Ordinal notation systems corresponding to Friedman's linearized well-partial-orders with gap-condition. Archive for Mathematical Logic, 56 (5-6). pp. 607-638. ISSN 0933-5846
Abstract
In this article we investigate whether the following conjecture is true or not: does the addition-free theta functions form a canonical notation system for the linear versions of Friedman’s well-partial-orders with the so-called gap-condition over a finite set of n labels. Rather surprisingly, we can show this is the case for two labels, but not for more than two labels. To this end, we determine the order type of the notation systems for addition-free theta functions in terms of ordinals less than ε0ε0 . We further show that the maximal order type of the Friedman ordering can be obtained by a certain ordinal notation system which is based on specific binary theta functions.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2017, Springer-Verlag Berlin Heidelberg. This is an author produced version of a paper published in Archive for Mathematical Logic. The final publication is available at Springer via https://doi.org/10.1007/s00153-017-0559-2. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Well-partial-orderings; Maximal order type; Gap-embeddability relation; Ordinal notation systems; Collapsing function |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 19 Jun 2017 10:42 |
Last Modified: | 02 Jun 2018 00:38 |
Status: | Published |
Publisher: | Springer Verlag |
Identification Number: | 10.1007/s00153-017-0559-2 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:117847 |