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Lowness for isomorphism, countable ideals, and computable traceability
Author(s) -
Franklin Johan. Y.,
Solomon Reed
Publication year - 2020
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201900066
Subject(s) - countable set , isomorphism (crystallography) , mathematics , ideal (ethics) , principal ideal , pure mathematics , traceability , discrete mathematics , combinatorics , statistics , crystallography , law , political science , prime (order theory) , chemistry , crystal structure
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.