Relations enumerable from positive information
Why this work is in the frame
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Bibliographic record
Abstract
Abstract We study countable structures from the viewpoint of enumeration reducibility. Since enumeration reducibility is based on only positive information, in this setting it is natural to consider structures given by their positive atomic diagram—the computable join of all relations of the structure. Fixing a structure ${\mathcal{A}}$, a natural class of relations in this setting are the relations $R$ such that $R^{\hat{\mathcal{A}}}$ is enumeration reducible to the positive atomic diagram of $\hat{\mathcal{A}}$ for every $\hat{\mathcal{A}}\cong{\mathcal{A}}$ – the relatively intrinsically positively enumerable (r.i.p.e.) relations. We show that the r.i.p.e. relations are exactly the relations that are definable by $\varSigma ^{p}_{1}$ formulas, a subclass of the infinitary $\varSigma ^{0}_{1}$ formulas. We then introduce a new natural notion of the jump of a structure and study its interaction with other notions of jumps.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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