## 351 Citations

### Reverse Mathematics and Algebraic Field Extensions

- MathematicsComput.
- 2013

This paper analyzes theorems about algebraic field extensions using the techniques of reverse mathematics. In section §2, we show that WKL0 is equivalent to the ability to extend F-automorphisms of…

### Generalized notions of mind change complexity

- Computer ScienceCOLT '97
- 1997

The notion of mind change bound for behaviourally correct learning is indirectly addressed by employing the above four types to restrict the number of predictive errors of commission in finite error next value learning (NV'') -- a model equivalent to behaviourallycorrect learning.

### Computability in Symbolic Dynamics

- MathematicsCiE
- 2016

We give an overview of the interplay between computability and symbolic dynamics. A multidimensional shift of finite type (SFT) is a set of colorings of Z given by local rules. SFTs are one of the…

### Weakly Represented Families in the Context of Reverse Mathematics

- Mathematics
- 2016

It is common pratice in computability theory to represent a family of objects by a single object; this is typically done in such a way that the individual members of the family can be derived in a…

### Jump inversions inside effectively closed sets and applications to randomness

- MathematicsThe Journal of Symbolic Logic
- 2011

Using techniques for coding information into incomplete randoms, a negative answer is given to [24, Problem 8.2.14]: not all weakly 2-random sets are array computable, given any oracle X, there is a weakly2-random which is not array Computable relative to X, which contrasts with the fact that all 2- random sets arearray computable.

## References

SHOWING 1-10 OF 19 REFERENCES

### The Completeness of the First-Order Functional Calculus

- MathematicsJ. Symb. Log.
- 1949

This paper presents a new method of proof for the first-order functional calculus which requires less formal development of the system from the axioms and suggests a new approach to the problem of completeness for functional calculi of higher order.

### A criterion for completeness of degrees of unsolvability

- MathematicsJournal of Symbolic Logic
- 1957

Kleene and Post [2] have shown that between each degree a and its completion a′ there are an infinity of mutually incomparable degrees of unsolvability, and that between a and its nth. completion…

### The class of recursive functions

- Mathematics
- 1958

In this note, we find the position of the predicate "a% is recursive" in the Kleene arithmetical hierarchy.' The proof involves a use of topology; the key step is the application of Baire's category…

### A theorem on minimal degrees

- Mathematics, Computer ScienceJournal of Symbolic Logic
- 1997

This paper proves that there is a recursively enumerable degree between 0 and 0′ and some obvious respects in which that set of all degrees differs from the set of recurring enumerable degrees; e.g., the former is uncountable and has no largest member.

### RECURSIVE AND RECURSIVELY ENUMERABLE ORDERS(

- Mathematics
- 1956

I. Basic concepts 1. Recursive enumerability and recursiveness. We consider infinite sequences of non-negative integers, free from repetitions. A familiar equivalence relation between such sequences…

### Recursively enumerable sets of positive integers and their decision problems

- Mathematics
- 1944

Introduction. Recent developments of symbolic logic have considerable importance for mathematics both with respect to its philosophy and practice. That mathematicians generally are oblivious to the…

### Borel sets and hyperdegrees

- MathematicsJournal of Symbolic Logic
- 1973

It is proved that any hyperdegree, in which the hyperjump is hyperarithmetic, forms a basis for the Δ 1 1 subsets of ω ω with no hyperar arithmetic elements.

### Sets with no subset of higher degree

- MathematicsJournal of Symbolic Logic
- 1969

This paper constructs an infinite set which is not recursive in any of its coinfinite subsets, and thus contains no subset of higher degree.

### A minimal pair of Π10 classes

- MathematicsJournal of Symbolic Logic
- 1971

A pair of sets (A0, A1) forms a minimal pair if A0 and A1 are nonrecursive, and if whenever a set B is recursive both in A0 and in A1 then B is recursive. C. E. M. Yates [8] and independently A. H.…

### Uniformly introreducible sets

- Mathematics, Computer ScienceJournal of Symbolic Logic
- 1969

“uniformly introreducible” sets (which will be defined in §2) are more tractable, and it turns out that some results on retraceable sets extend to uniformly introreduceable sets while others fail.