On Computable Automorphisms of The Rational Numbers
نویسندگان
چکیده
The relationship between ideals I of Turing degrees and groups of I{recursive automorphisms of the ordering on rationals is studied. We discuss the diierences between such groups and the group of all auto-morphisms, prove that the isomorphism type of such a group completely deenes the ideal I, and outline a general correspondence between principal ideals of Turing degrees and the rst{order properties of such groups.
منابع مشابه
On the Monotonic Computability of Semi-computable Real Numbers
Let h : N → Q be a computable function. A real number x is h-monotonically computable (h-mc, for short) if there is a computable sequence (xs) of rational numbers which converges to x in such a way that the ratios of the approximation errors are bounded by h. In this paper we discuss the h-monotonic computability of semi-computable real numbers which are limits of monotone computable sequences ...
متن کاملOn the Weak Computability of Continuous Real Functions
In computable analysis, sequences of rational numbers which effectively converge to a real number x are used as the (ρ-) names of x. A real number x is computable if it has a computable name, and a real function f is computable if there is a Turing machine M which computes f in the sense that, M accepts any ρ-name of x as input and outputs a ρ-name of f (x) for any x in the domain of f . By wea...
متن کاملE 2 - computability of e , π and other famous constants
We show that e, π and other remarkable real numbers are limits of E-computable sequences of rational numbers having a polynomial rate of convergence (as usual, E denotes the second Grzegorczyk class). However, only the rational numbers are limits of E-computable sequences of rational numbers with an exponential rate of convergence
متن کاملWeakly Computable Real Numbers
A real number x is recursively approximable if it is a limit of a computable sequence of rational numbers. If, moreover, the sequence is increasing (decreasing or simply monotonic), then x is called left computable (right computable or semicomputable). x is called weakly computable if it is a difference of two left computable real numbers. We show that a real number is weakly computable if and ...
متن کاملOn the Subrecursive Computability of Several Famous Constants
For any class F of total functions in the set N of the natural numbers, we define the notion of F-computable real number. A real number α is called Fcomputable if there exist one-argument functions f , g and h in F such that for any n in N the distance between the rational number f(n) − g(n) over h(n) + 1 and the number α is not greater than the reciprocal of n + 1. Most concrete real numbers p...
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 66 شماره
صفحات -
تاریخ انتشار 2001