Recursively Inseparable Sets
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In computability theory, recursively inseparable sets are pairs of sets of natural numbers that cannot be "separated" with a computable set (Monk 1976, p. 100). These sets arise in the study of computability theory itself, particularly in relation to 01 classes. Recursively inseparable sets also arise in the study of Gödel's incompleteness theorem. The natural numbers are the set = {0, 1, 2, ...}. Given subsets A and B of , a separating set C is a subset of such that…mehr

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In computability theory, recursively inseparable sets are pairs of sets of natural numbers that cannot be "separated" with a computable set (Monk 1976, p. 100). These sets arise in the study of computability theory itself, particularly in relation to 01 classes. Recursively inseparable sets also arise in the study of Gödel's incompleteness theorem. The natural numbers are the set = {0, 1, 2, ...}. Given subsets A and B of , a separating set C is a subset of such that A C and B C = . For example, if A and B are disjoint then A itself is a separating set for the pair, as is B. If a pair of disjoint sets A and B has no computable separating set, then the two sets are recursively inseparable.