We consider two variants of strongly bounded Turing reductions: An identity bounded Turing reduction
(ibTreduction for short) is a Turing reduction where no oracle query is greater than the input while a computable
Lipschitz reduction (clreduction for short) is a Turing reduction where the oracle queries on input x are bounded
by x+c for some constant c. Since ibTreducibility is stronger than clreducibility and clreducibility is stronger
than wttreducibility (where a weak truthtable (wtt) reduction is a Turing reduction where the oracle queries are
computably bounded in the inputs) we may look at the partial ordering of the computably enumerable (c.e.)
ibTdegrees inside the cldegree of a noncomputable c.e. set A and, similarly, at the partial ordering of the c.e.
cldegrees inside the wttdegree of a noncomputable c.e. set A. In our talk we discuss some properties of these
partial orderings.
