Bibliographic Details
| Title: |
Failure modes for structural highness notions. |
| Authors: |
Calvert, Wesley1 (AUTHOR), Franklin, Johanna N Y2 (AUTHOR), Turetsky, Dan3 (AUTHOR) |
| Source: |
Journal of Logic & Computation. Oct2025, Vol. 35 Issue 7, p1-17. 17p. |
| Subjects: |
Computable functions, Isomorphism (Mathematics), Scholarly method |
| Abstract: |
In Calvert, Franklin, and Turetsky (2023, J. Symb. Log. 88, 1692–1724), we defined several classes of degrees that are high in senses related to computable structure theory. Each class of degrees is characterized by a structural feature (e.g. an isomorphism) that it can compute if such a feature exists. In this paper, we examine each of these classes and characterize them based on what they do if no such object exists. We describe, in particular, reticent, loquacious and collegiate senses of being high. These, respectively, reflect the case where a computation from the degree will give output only if the desired feature exists, the case where it will give output of some kind whether or not the feature exists, and the case where the degree will compute either the feature or the best available approximation to it. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
