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

  • Denis R. Hirschfeldt (a1), Bakhadyr Khoussainov (a2) and Richard A. Shore (a3)

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.

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[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.
[2] Ershov, Y. L., Goncharov, S. S., Nerode, A., and Remmel, J. B. (editors). Handbook of recursive mathematics. Studies in Logic and the Foundations of Mathematics, vol, 138-139, Elsevier Science. Amsterdam, 1998.
[3] Goncharov, S. S., Computable single-valued numerations. Algebra and Logic, vol. 19 (1980), pp. 325356.
[4] Goncharov, S. S., Problem of the number of non-self-equivalent constructivizations. Algebra and Logic, vol. 19 (1980), pp. 401414.
[5] Harizanov, V. S., Pure computable model theory, in Ershov, et al. [2], pp. 3114.
[6] Hirschfeldt, D. R., Degree spectra of intrinsically c. e. relations, this Journal, vol. 66 (2001), pp. 441469.
[7] Hirschfeldt, D. R., Degree spectra of relations on structures of finite computable dimension. Annals of Pure and Applied Logic, vol. 115 (2002), pp. 233277.
[8] Hirschfeldt, D. R., Khoussainov, B., Shore, R. A., and Slinko, A. M., Degree spectra and computable dimension in algebraic structures. Annals of Pure and Applied Logic, vol. 115 (2002), pp. 71113.
[9] Khoussainov, B. and Shore, R. A., Computable isomorphisms, degree spectra of relations, and Scott families. Annals of Pure and Applied Logic, vol. 93 (1998), pp. 153193.
[10] Khoussainov, B. and Shore, R. A., Effective model theory: the number of models and their complexity, Models and computability (Cooper, S. B. and Truss, J. K., editors), London Mathematical Society Lecture Note Series, vol. 259, Cambridge University Press, Cambridge, 1999, pp. 193239.
[11] Millar, T., Recursive categoricity and persistence, this Journal, vol. 51 (1986), pp. 430434.
[12] Soare, R. I., Recursively enumerable sets and degrees, Perspectives in Mathematical Logic, Springer-Verlag, Heidelberg, 1987.

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