Bibliographic record
Abstract
Abstract In the topological semantics, quantified intuitionistic logic, QH, is known to be strongly complete not only for the class of all topological spaces but also for some particular topological spaces — for example, for the irrational line, ${\Bbb P}$ , and for the rational line, ${\Bbb Q}$ , in each case with a constant countable domain for the quantifiers. Each of ${\Bbb P}$ and ${\Bbb Q}$ is a separable zero-dimensional dense-in-itself metrizable space. The main result of the current article generalizes these known results: QH is strongly complete for any zero-dimensional dense-in-itself metrizable space with a constant domain of cardinality ≤ the space’s weight; consequently, QH is strongly complete for any separable zero-dimensional dense-in-itself metrizable space with a constant countable domain. We also prove a result that follows from earlier work of Moerdijk: if we allow varying domains for the quantifiers, then QH is strongly complete for any dense-in-itself metrizable space with countable domains.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.004 | 0.007 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".