Degrees of categoricity above limit ordinals
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
A computable structure [Formula: see text] has degree of categoricity d if d is exactly the degree of difficulty of computing isomorphisms between isomorphic computable copies of [Formula: see text]. Fokina, Kalimullin, and Miller showed that every degree d.c.e. in and above [Formula: see text], for any [Formula: see text], and also the degree [Formula: see text], are degrees of categoricity. Later, Csima, Franklin, and Shore showed that every degree [Formula: see text] for any computable ordinal α, and every degree d.c.e. in and above [Formula: see text] for any successor ordinal α, is a degree of categoricity. We show that every degree c.e. in and above [Formula: see text], for α a limit ordinal, is a degree of categoricity. We also show that every degree c.e. in and above [Formula: see text] is the degree of categoricity of a prime model, making progress towards a question of Bazhenov and Marchuk.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.007 | 0.015 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it