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Jun 23, 2016 at 21:44 comment added Payam Seraji Sorry, there was a mistake and some 3's should be in fact be 4 and the last 4 should be 5....I corrected them.
Jun 23, 2016 at 21:07 comment added Payam Seraji Yes, you are right....but what I had in mind was Turing degree of the function $f$ as a r.e. set (i.e. Turing degree of its graph). Graph of the function you described is $0^{(3)}$-r.e., but its Turing degree may be bigger than $0^{(3)}$. I edited the question to make this point clear.
Jun 23, 2016 at 8:16 history answered Bjørn Kjos-Hanssen CC BY-SA 3.0