Ordinal notation systems corresponding to Friedman's linearized well-partial-orders with gap-condition [article]

Michael Rathjen, Jeroen Van der Meeren, Andreas Weiermann
2015 arXiv   pre-print
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 ε_0. We further show that the maximal order
more » ... type of the Friedman ordering can be obtained by a certain ordinal notation system which is based on specific binary theta functions.
arXiv:1505.01359v1 fatcat:qvtn4hwggnckxeykoz7w5iwcaq