Enumeration reducibility and partial degrees

Enumeration Reducibility, Nondeterministic Computations and Relative Computability of Partial Functions

In a computation using auxiliary informational inputs one can think of the external resource making itself available in different ways. One way is via an oracle as in Turing reducibility, where information is supplied on demand without any time delay. Alternatively the Scott graph model for lambda calculus suggests a situation where new information, only some of it immediately related to the cu...

Embedding countable partial orderings in the enumeration degrees and the ω-enumeration degrees

One of the most basic measures of the complexity of a given partially ordered structure is the quantity of partial orderings embeddable in this structure. In the structure of the Turing degrees, DT , this problem is investigated in a series of results: Mostowski [15] proves that there is a computable partial ordering in which every countable partial ordering can be embedded. Kleene and Post [10...

Symmetric Enumeration Reducibility

Enumeration Order Reducibility

In this article we define a new reducibility based on enumeration orders.

Enumeration Reducibility and Computable Structure Theory

In classical computability theory the main underlying structure is that of the natural numbers or equivalently a structure consisting of some constructive objects, such as words in a finite alphabet. In the 1960’s computability theorists saw it as a challenge to extend the notion of computable to arbitrary structure. The resulting subfield of computability theory is commonly referred to as comp...