A real is called recursively enumerable if it is the limit of a recursive, increasing, converging sequence of rationals. Following Solovay (unpublished manuscript, IBM Thomas J. Watson Research… (More)

Partially supported by a Mathematical Sciences Postdoctoral Research Fellowship and ARO through MSI, Cornell University, DALL03-91-C0027 Partially supported by ISF, NQ6000 and NQ6300, and by ARO… (More)

Whenever a structure with a particularly interesting computability-theoretic property is found, it is natural to ask whether similar examples can be found within well-known classes of algebraic… (More)

It is shown that the parity game can be solved in quasipolynomial time. The parameterised parity game â with <i>n</i> nodes and <i>m</i> distinct values (aka colours or priorities) â is proven to… (More)

A real is computable if its left cut, L( ); is computable. If (qi)i is a computable sequence of rationals computably converging to ; then fqig; the corresponding set, is always computable. A… (More)

The spectrum of a relation L% on a computable structure is the set of Turing degrees of the image of R under all isomorphisms between LZZ and any other computable structure g. The relation .%’ is… (More)

In this paper we investigate computable models of א1-categorical theories and Ehrenfeucht theories. For instance, we give an example of an א1categorical but not א0-categorical theory T such that all… (More)

We investigate partial orders that are computable, in a precise sense, by finite automata. Our emphasis is on trees and linear orders. We study the relationship between automatic linear orders and… (More)