Co-ordering and Type 2 co-ordering

In [arXiv:1006.4939] the enumeration order reducibility is defined on natural numbers. For a c.e. set A, [A] denoted the class of all subsets of natural numbers which are co-order with A. In definition 5 we redefine co-ordering for rational numbers. One of the main questions there, was: "For a specific c.e. set A, consider set of all enumerations of it which is generated by some Turing machine {TMA} what are the associated order types in [A]?" Here, we propose the same question for rational numbers, and we try to investigate the varieties of c.e. sets on Q. The theories here are hold for Rc and we could repeat the same theories in this domain, in a parallel way.