Ordinal notation systems corresponding to Friedman’s linearized well-partial-orders with gap-condition

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 ca...

Full description

Saved in:
Bibliographic Details
Published in:Archive for mathematical logic 2017-08, Vol.56 (5-6), p.607-638
Main Authors: Rathjen, Michael, Van der Meeren, Jeroen, Weiermann, Andreas
Format: Article
Language:English
Subjects:
Algebra
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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 ε 0 . 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.
ISSN:0933-5846
1432-0665
DOI:10.1007/s00153-017-0559-2