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Lowness for isomorphism, countable ideals, and computable traceability
Mathematical Logic Quarterly 66 (1):104-114 (2020)
Abstract
We show that every countable ideal of degrees that are low for isomorphism is contained in a principal ideal of degrees that are low for isomorphism by adapting an exact pair construction. We further show that within the hyperimmune free degrees, lowness for isomorphism is entirely independent of computable traceability.Other Versions
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Citations of this work
Structural Highness Notions.Wesley Calvert, Johanna N. Y. Franklin & Dan Turetsky - 2023 - Journal of Symbolic Logic 88 (4):1692-1724.
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.
Computational randomness and lowness.Sebastiaan Terwijn & Domenico Zambella - 2001 - Journal of Symbolic Logic 66 (3):1199-1205.
Recursively enumerable sets modulo iterated jumps and extensions of Arslanov's completeness criterion.C. G. Jockusch, M. Lerman, R. I. Soare & R. M. Solovay - 1989 - Journal of Symbolic Logic 54 (4):1288-1323.
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