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A computably categorical structure whose expansion by a constant has infinite computable dimension

Published online by Cambridge University Press:  12 March 2014

Denis R. Hirschfeldt
Affiliation:
Department of Mathematics, University of Chicago, Chicago, Illinois 60637, USA
Bakhadyr Khoussainov
Affiliation:
Department of Computer Science, University of Auckland, Private Bag 92019, Auckland, New Zealand
Richard A. Shore
Affiliation:
Department of Mathematics, Cornell University, Ithaca, New York 14853, USA

Abstract

Cholak, Goncharov, Khoussainov, and Shore [1] showed that for each k > 0 there is a computably categorical structure whose expansion by a constant has computable dimension k. We show that the same is true with k replaced by ω. Our proof uses a version of Goncharov's method of left and right operations.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2003

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References

[1] Cholak, P., Goncharov, S. S.. Khoussainov, B.. and Shore, R. A., Computably categorical structures and expansions by constants, this Journal, vol. 64 (1999), pp. 1337.Google Scholar
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