Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  define the notion of indifferent set with respect to a given class of {0,1}-sequences. Roughly, for a set A in the class, a set of natural numbers I is indifferent for A with respect to the class if it does not matter how  change A at the positions in I: the new sequence continues to be in the given class.  are especially interested in studying those sets that are indifferent with respect to classes containing different types of stochastic sequences. For the class of Martin-Lof random sequences,  show that every random sequence has an infinite indifferent set and that there is no universal indifferent set.  show that indifferent sets must be sparse, in fact sparse enough to decide the halting problem.  prove the existence of co-c.e. indifferent sets, including a co-c.e. set that is indifferent for every 2-random sequence with respect to the class of random sequences. For the class of absolutely normal numbers,  show that there are computable indifferent sets with respect to that class and  conclude that there is an absolutely normal real number in every non-trivial many-one degree.
['Santiago Figueira', 'Joseph S. Miller', 'André Nies']
I am writing a research paper on a idea Indifferent Sets
[{"from": "human", "value": "I am writing a research paper on a idea Indifferent Sets"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  define the notion of indifferent set with respect to a given class of {0,1}-sequences. Roughly, for a set A in the class, a set of natural numbers I is indifferent for A with respect to the class if it does not matter how  change A at the positions in I: the new sequence continues to be in the given class.  are especially interested in studying those sets that are indifferent with respect to classes containing different types of stochastic sequences. For the class of Martin-Lof random sequences,  show that every random sequence has an infinite indifferent set and that there is no universal indifferent set.  show that indifferent sets must be sparse, in fact sparse enough to decide the halting problem.  prove the existence of co-c.e. indifferent sets, including a co-c.e. set that is indifferent for every 2-random sequence with respect to the class of random sequences. For the class of absolutely normal numbers,  show that there are computable indifferent sets with respect to that class and  conclude that there is an absolutely normal real number in every non-trivial many-one degree."}]