User blog:LittlePeng9/Binary relations via Turing machines

Here I want to propose how to give any Turing machine a corresponding binary relation R. Of course, a subsets of set of all relations are sets of partial orders, total orders and, most importantly, well orders. Thus we have alternative to Kleene's O correspondence of ordinals to machines.

Definition
Let us have any fixed Turing machine M. Corresponding relation R is defined on \(\mathbb{N}^2\) as follows: xRy iff machine M halts on input 1x_1y.

(Examples yet to come)