On the role of the collection principle for Σ⁰₂-formulas in second-order reverse mathematics
Bibliographic record
Abstract
We show that the principle P A R T \mathsf {PART} from Hirschfeldt and Shore is equivalent to the Σ 2 0 \Sigma ^0_2 -Bounding principle B Σ 2 0 B\Sigma ^0_2 over R C A 0 \mathsf {RCA}_0 , answering one of their open questions. Furthermore, we also fill a gap in a proof of Cholak, Jockusch and Slaman by showing that D 2 2 D^2_2 implies B Σ 2 0 B\Sigma ^0_2 and is thus indeed equivalent to Stable Ramsey’s Theorem for Pairs ( S R T 2 2 \mathsf {SRT}^2_2 ). This also allows us to conclude that the combinatorial principles I P T 2 2 \mathsf {IPT}^2_2 , S P T 2 2 \mathsf {SPT}^2_2 and S I P T 2 2 \mathsf {SIPT}^2_2 defined by Dzhafarov and Hirst all imply
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.007 | 0.011 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.004 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.004 | 0.011 |
| Scholarly communication | 0.006 | 0.023 |
| Open science | 0.003 | 0.007 |
| Research integrity | 0.002 | 0.007 |
| Insufficient payload (model declined to judge) | 0.014 | 0.005 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".