Low upper bounds in the Turing degrees revisited
نویسندگان
چکیده
We give an alternative proof of a result of Kučera and Slaman (2009, Lower upper bounds of ideals, Journal of Symbolic Logic, 74, 517–534) on low bounds of ideals in the 2 Turing degrees. This is a characterization of the ideals in the 0 2 degrees which have a low upper bound. It follows that there is a low upper bound for the ideal of the K-trivial degrees. Our proof is direct, in the sense that it does not use universal classes of PA degrees.
منابع مشابه
Some improvements in fuzzy turing machines
In this paper, we improve some previous definitions of fuzzy-type Turing machines to obtain degrees of accepting and rejecting in a computational manner. We apply a BFS-based search method and some level’s upper bounds to propose a computational process in calculating degrees of accepting and rejecting. Next, we introduce the class of Extended Fuzzy Turing Machines equipped with indeterminacy s...
متن کاملUpper bounds on ideals in the computably enumerable Turing degrees
We study ideals in the computably enumerable Turing degrees, and their upper bounds. Every proper Σ0 4 ideal in the c.e. Turing degrees has an incomplete upper bound. It follows that there is no Σ0 4 prime ideal in the c.e. Turing degrees. This answers a question of Calhoun (1993) [2]. Every properΣ0 3 ideal in the c.e. Turing degrees has a low2 upper bound. Furthermore, the partial order of Σ0...
متن کاملOn minimal degree simultaneous pole assignment problems
In this paper, we show that a generic r-tuple of m-input p-output linear systems is simultaneously pole assignable if r < m+ p and the McMillan degrees of the systems are not too different. We also obtain upper bounds for the degrees of the compensators which simultaneously assign the characteristic polynomials of the r-tuple of closed loop systems. The upper bounds are obtained for each of the...
متن کاملEventually Infinite Time Turing Machine Degrees: Infinite Time Decidable Reals
We characterise explicitly the decidable predicates on integers of Innnite Time Turing machines, in terms of admissibility theory and the constructible hierarchy. We do this by pinning down , the least ordinal not the length of any eventual output of an Innnite Time Turing machine (halting or otherwise); using this the Innnite Time Turing Degrees are considered, and it is shown how the jump ope...
متن کاملIncompleteness, Approximation and Relative Randomness
We present some results about the structure of c.e. and ∆2 LR-degrees. First we give a technique for lower cone avoidance in the c.e. and ∆2 LR-degrees, and combine this with upper cone avoidance via Sacks restraints to construct a c.e. LR-degree which is incomparable with a given intermediate ∆2 LR-degree. Next we combine measure-guessing with an LR-incompleteness strategy to construct an inco...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Log. Comput.
دوره 22 شماره
صفحات -
تاریخ انتشار 2012