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2 results on '"03F15, 03E10, 06A06"'

1. Ordinal notation systems corresponding to Friedman's linearized well-partial-orders with gap-condition

Author

Rathjen, Michael, Van der Meeren, Jeroen, and Weiermann, Andreas

Subjects
Mathematics - Logic, 03F15, 03E10, 06A06
Abstract

In this article we investigate whether 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 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 $\varepsilon_0$. 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., Comment: 41 pages

Published
2015

2. Ordinal notation systems corresponding to Friedman's linearized well-partial-orders with gap-condition

Author

Andreas Weiermann, Michael Rathjen, and Jeroen Van der Meeren

Subjects
Set-builder notation, Discrete mathematics, Abuse of notation, Multi-index notation, Logic, Big O notation, 010102 general mathematics, Ordinal analysis, Limit ordinal, Mathematics - Logic, 0102 computer and information sciences, 01 natural sciences, 03F15, 03E10, 06A06, Philosophy, 010201 computation theory & mathematics, Big O in probability notation, FOS: Mathematics, 0101 mathematics, Logic (math.LO), Ordinal notation, Mathematics
Abstract

In this article we investigate whether 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 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 $\varepsilon_0$. 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., Comment: 41 pages

Published
2015
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