Bibliographic record
Abstract
We study capturing construction schemes, a new combinatorial tool introduced by Todorcevic to build uncountable structures. It consists of a ranked family of finite sets that provides a framework to do recursive constructions of uncountable objects by working with finite amalgamations of finite isomorphic substructures, the uncountable substructures of the final object can be further studied using capturing. In this Thesis we study the consistency of capturing construction schemes, and related definitions, we prove results of consistency, and give several applications of this tool both to infinite combinatorics and Banach space theory. For example, we show weaker forms of capturing, such as n-capturing, form a strict hierarchy which is related to the m-Knaster Hierarchy. We also show how capturing construction schemes can be used in constructing Suslin trees and Hausdorff gaps of a special kind in an intuitive manner. And give some applications to the theory of nonseparable Banach spaces.
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How this classification was reachedexpand
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 | 0.000 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".