منابع مشابه
Countable Thin Π 01 Classes
A Π1 class P ⊂ {0, 1} ω is thin if every Π1 subclass Q of P is the intersection of P with some clopen set. Countable thin Π1 classes are constructed having arbitrary recursive Cantor-Bendixson rank. A thin Π1 class P is constructed with a unique nonisolated point A of degree 0′. It is shown that, for all ordinals α > 1, no set of degree ≥ 0′′ can be a member of any thin Π1 class. An r.e. degree...
متن کاملNon-branching degrees in the Medvedev lattice of Π01 classes
Special thanks to my advisor Steffen Lempp for his guidance and conversation. Abstract Always Sometimes 2 In this talk I will present the necessary background and then describe and characterize the non-branching degrees. Significantly, I will show three distinct classes of non-branching degrees. The Medvedev lattice of Π 0 1 classes is a lattice of certain subsets of 2 ω under a natural reducti...
متن کاملΠ01 Classes, Peano Arithmetic, Randomness, and Computable Domination
We present an overview of the topics in the title and of some of the key results pertaining to them. These have historically been topics of interest in computability theory and continue to be a rich source of problems and ideas. In particular, we draw attention to the links and connections between these topics and explore their significance to modern research in the field.
متن کاملThin classes of separating sets
There are various definitions for a Martin–Pour-El theory in the literature. We isolate two such definitions: weak Martin–Pour-El theories (which correspond to perfect thin Π1 classes) and strong Martin–Pour-El theories (which correspond to thin classes of separating sets). By concentrating on constructions of appropriate Π1 classes, rather than on direct constructions of the theories, we show ...
متن کاملΣ01 and Π01 equivalence structures
We study computability theoretic properties of 01 and 0 1 equivalence structures and how they di er from computable equivalence structures or equivalence structures that belong to the Ershov di erence hierarchy. This includes the complexity of isomorphisms between 01 equivalence structures and between 01 equivalence structures. Any 0 1 equivalence structure A with in nitely many in nite equival...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 1993
ISSN: 0168-0072
DOI: 10.1016/0168-0072(93)90001-t