منابع مشابه
Immunity and Non-Cupping for Closed Sets
We extend the notion of immunity to closed sets and to Π1 classes in particular in two ways: immunity meaning the corresponding tree has no infinite computable subset, and tree-immunity meaning it has no infinite computable subtree. We separate these notions from each other and that of being special, and show separating classes for computably inseparable c.e. sets are immune and perfect thin cl...
متن کاملImmunity for Closed Sets
The notion of immune sets is extended to closed sets and Π 1 classes in particular. We construct aΠ 1 class with no computable member which is not immune. We show that for any computably inseparable sets A and B, the class S(A,B) of separating sets for A and B is immune. We show that every perfect thin Π 1 class is immune. We define the stronger notion of prompt immunity and construct an exampl...
متن کاملCupping with Random Sets
We prove that a set is K-trivial if and only if it is not weakly ML-cuppable. Further, we show that a set below zero jump is K-trivial if and only if it is not ML-cuppable. These results settle a question of Kučera, who introduced both cuppability notions.
متن کاملNon-cupping and Randomness
Let Y ∈ ∆2 be Martin-Löf-random. Then there is a promptly simple set A such that for each Martin-Löf-random set Z, Y ≤T A ⊕ Z ⇒ Y ≤T Z. When Y = Ω, one obtains a c.e. non-computable set A which is not weakly Martin-Löf cuppable. That is, for any Martin-Löf-random set Z, if ∅′ ≤T A⊕ Z, then ∅′ ≤T Z.
متن کاملMinimal closed sets and maximal closed sets
Some properties of minimal open sets and maximal open sets are studied in [1, 2]. In this paper, we define dual concepts of them, namely, maximal closed set and minimal closed set. These four types of subsets appear in finite spaces, for example. More generally, minimal open sets and maximal closed sets appear in locally finite spaces such as the digital line. Minimal closed sets and maximal op...
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ژورنال
عنوان ژورنال: Tbilisi Mathematical Journal
سال: 2009
ISSN: 1875-158X
DOI: 10.32513/tbilisi/1528768843