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A computably categorical structure whose expansion by a constant has infinite computable dimension
Journal of Symbolic Logic 68 (4):1199-1241 (2003)
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 operationsDOI
10.2178/jsl/1067620182
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Citations of this work
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References found in this work
Degree spectra and computable dimensions in algebraic structures.Denis R. Hirschfeldt, Bakhadyr Khoussainov, Richard A. Shore & Arkadii M. Slinko - 2002 - Annals of Pure and Applied Logic 115 (1-3):71-113.
Computably categorical structures and expansions by constants.Peter Cholak, Sergey Goncharov, Bakhadyr Khoussainov & Richard A. Shore - 1999 - Journal of Symbolic Logic 64 (1):13-37.
Computable isomorphisms, degree spectra of relations, and Scott families.Bakhadyr Khoussainov & Richard A. Shore - 1998 - Annals of Pure and Applied Logic 93 (1-3):153-193.
Degree spectra of intrinsically C.e. Relations.Denis R. Hirschfeldt - 2001 - Journal of Symbolic Logic 66 (2):441-469.
Degree spectra of relations on structures of finite computable dimension.Denis R. Hirschfeldt - 2002 - Annals of Pure and Applied Logic 115 (1-3):233-277.
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