On the construction of effectively random sets
نویسندگان
چکیده
We present a comparatively simple way to construct MartinLöf random and rec-random sets with certain additional properties, which works by diagonalizing against appropriate martingales. Reviewing the result of Gács and Kučera, for any given set X we construct a Martin-Löf random set from which X can be decoded effectively. By a variant of the basic construction we obtain a rec-random set that is weak truth-table autoreducible and we observe that there are MartinLöf random sets that are computably enumerable self-reducible. The two latter results complement the known facts that no rec-random set is truth-table autoreducible and that no Martin-Löf random set is Turingautoreducible [8, 24].
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عنوان ژورنال:
- J. Symb. Log.
دوره 69 شماره
صفحات -
تاریخ انتشار 2004