Every 1-generic computes a properly 1-generic
نویسندگان
چکیده
A real is called properly n-generic if it is n-generic but not n + 1generic. We show that every 1-generic real computes a properly 1-generic real. On the other hand, if m > n > 2 then an m-generic real cannot compute a properly n-generic real.
منابع مشابه
Enumeration 1-genericity in the Local Enumeration Degrees
We discuss a notion of forcing that characterises enumeration 1genericity and we investigate the immunity, lowness and quasiminimality properties of enumeration 1-generic sets and their degrees. We construct an enumeration operator ∆ such that, for any A, the set ∆ is enumeration 1-generic and has the same jump complexity as A. We also prove that every nonzero ∆ 2 degree bounds a nonzero enumer...
متن کاملGenerics for computable Mathias forcing
We study the complexity of generic reals for computable Mathias forcing in the context of computability theory. The n-generics and weak ngenerics form a strict hierarchy under Turing reducibility, as in the case of Cohen forcing. We analyze the complexity of the Mathias forcing relation, and show that if G is any n-generic with n ≥ 3 then it satisfies the jump property G(n−1) ≡T G′ ⊕ ∅(n). We p...
متن کاملOn Mathias Generic Sets
We present some results about generics for computable Mathias forcing. The n-generics and weak n-generics in this setting form a strict hierarchy as in the case of Cohen forcing. We analyze the complexity of the Mathias forcing relation, and show that if G is any n-generic with n ≥ 3 then it satisfies the jump property G(n−1) = G′ ⊕ ∅(n). We prove that every such G has generalized high degree, ...
متن کاملThe Finite Intersection Principle and Genericity
We show that a ∆2 Turing degree computes solutions to all computable instances of the finite intersection principle if and only if it computes a 1-generic degree. We also investigate finite and infinite variants of the prin-
متن کاملEffect generic and non-generic feedback on Motor Learning basketball free throw in Children
Non-generic feedback refers to a specific event and that task performance is the reason to the acquisition of skills and implies that performance is malleable, while generic feedback implies that task performance reflects an inherent ability. The Goal of this study was to determine the generic and non-generic feedback effects on children’s motor learning basketball free throw. This research was...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Symb. Log.
دوره 71 شماره
صفحات -
تاریخ انتشار 2006