# Is there a name for this infinite language?

Is there a name for this infinite language?

$$L = \{ 0(,1)^*(,2)^*(,3)^*....(,n)^* \;\mid n \geq 1\}$$

A string $w \in L$ is simply an ordered list of increasing integers in which every integer $\geq 1$ can be repeated 0 or more times, for example "0", "0,1", "0,1,2,2", "0,1,2,3", "0,1,1,4,4,4,21,21".

Or perhaps a name for its unary variant: $L_U = \{ 1^{x_1}(,1^{x_1})^*,1^{x_2}(,1^{x_2})^*,...,1^{x_n}(,1^{x_n})^* \mid x_1<x_2<...<x_n\}$