A reducibility condition for recursiveness

A World Where Relative Definability Coincides With Relative Recursiveness (i.e., Turing Reducibility)

A COMMUTATIVITY CONDITION FOR RINGS

In this paper, we use the structure theory to prove an analog to a well-known theorem of Herstein as follows: Let R be a ring with center C such that for all x,y ? R either [x,y]= 0 or x-x [x,y]? C for some non negative integer n= n(x,y) dependingon x and y. Then R is commutative.

Bounded Limit Recursiveness

Let X be a Turing oracle. A function f(n) is said to be boundedly limit recursive in X if it is the limit of an X-recursive sequence of X-recursive functions f̃(n, s) such that the number of times f̃(n, s) changes is bounded by a recursive function of n. Let us say that X is BLR-low if every function which is boundedly limit recursive in X is boundedly limit recursive in 0. This is a lowness prop...

Informational Recursiveness Against Singularity

The paper describes the arriving, the probable and the inevitable, emerging through the exponential technological development, particularly the informational one (IT), and by the new concepts of Kurzweil’s singularity of the strong artificial intelligence (AI) on the one side and by the recursiveness of author’s informational consciousness (IC) on the other. A comparison between the criteria of...

Associativeness versus Recursiveness

AbsikactFuzzy connectives use to be assumed associative. In this way, key operational difficulties are solved by means of a single binary operator. In this paper we point out that the main property in order to assure operativeness should be recurszveness, which is weaker than associativity. If calculus can be obtained by means of a recursive application of a sequence of binary connectives, we s...