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Taking the path computably traveled. (English) Zbl 1444.03139
Summary: We define a real \(A\) to be low for paths in Baire space (or Cantor space) if every \(\varPi^0_1\) class with an \(A\)-computable element has a computable element. We prove that lowness for paths in Baire space and lowness for paths in Cantor space are equivalent and, furthermore, that these notions are also equivalent to lowness for isomorphism.
MSC:
03D45 Theory of numerations, effectively presented structures
03D25 Recursively (computably) enumerable sets and degrees
03D28 Other Turing degree structures
03C57 Computable structure theory, computable model theory
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