On Computability Theoretic Properties of Structures and Their Cartesian Products

Abstract

In this paper we show that for any set X ⊆ ω there exists a structure A that has no presentation computable in X such that A 2 has a computable presentation. We also show that there exists a structure A with infinitely many computable isomorphism types such that A 2 has exactly one computable isomorphism type.Mathematics Subject Classification: 03D45, 03C57, 03D25.