Mathematical Logic Quarterly 46 (4):467-476 (2000)

Abstract
In this paper we show that for any set X ⊆ ω there exists a structure [MATHEMATICAL SCRIPT CAPITAL A] that has no presentation computable in X such that [MATHEMATICAL SCRIPT CAPITAL A]2 has a computable presentation. We also show that there exists a structure [MATHEMATICAL SCRIPT CAPITAL A] with infinitely many computable isomorphism types such that [MATHEMATICAL SCRIPT CAPITAL A]2 has exactly one computable isomorphism type
Keywords Computable structure  Computable isomorphism  Computable set
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DOI 10.1002/1521-3870(200010)46:4
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