Bibliographic record
Abstract
What largeness and structural assumptions on A ⊆ [ R ] ω A \subseteq [\mathbb {R}]^{\omega } can guarantee the existence of a non-empty perfect set P ⊆ R P \subseteq \mathbb {R} such that [ P ] ω ⊆ A [P]^{\omega } \subseteq A ? Such a set P P is called A A -homogeneous. We show that even if A A is open, in general it is independent of ZFC whether for a cardinal κ \kappa , the existence of an A A -homogeneous set H ∈ [ R ] κ H \in [\mathbb {R}]^{\kappa } implies the existence of a non-empty perfect A A -homogeneous set. On the other hand, we prove an infinite dimensional analogue of Mycielski’s Theorem: if A A is large in the sense of a suitable Baire category-like notion, then there exists a non-empty perfect A A -homogeneous set. We introduce fusion games to prove this and other infinite dimensional perfect set theorems. Finally we apply this theory to show that it is independent of ZFC whether Tukey reductions of the maximal analytic cofinal type can be witnessed by definable Tukey maps.
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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 | 0.003 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.005 | 0.011 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.016 | 0.003 |
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".