Given a countable and infinite set M. How does one call the class of orders on M that are induced by an enumeration of it?
For example the class of total orders does not capture what I mean, as with $M:=\{0,1\}^*$ starting with 0 < 00 < 000 < ... and then after that in the order the binary numbers ordered by their value, would be a total order, yet not such an "enumeration order".
Thanks in advance