Reed Solomon : A computably categorical structure with no Scott family of finitary formulas

Posted by , part of the Logic Seminar.

At

April 27, 2010, 4 p.m.

In

SEO 612

Abstract

A computable structure A is called computably categorical if for every computable structure B which is isomorphic to A, there is a computable isomorphism between A and B. Similarly, a computable structure A is called relatively computable categorical if for every isomorphic copy B (not necessarily computable), there is an isomorphism between A and B computable in the degree of B. It is known that relatively computably categorical structures have particularly simple Scott families consisting of finitary formulas. We construct an example showing that this property can fail as badly as possible for computable categorical structures.

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