Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
The infinite in mathematics has two manifestations. Its occurrence in analysis has been satisfactorily formalized and demystified by the -δ method of Bolzano, Cauchy and Weierstrass. It is of course the ‘set-theoretic infinite ’ that concerns me here. Once the existence of an infinite set is ac-cepted, the axioms of set theory imply the existence of a transfinite hierar-chy of larger and larger orders of infinity. I shall review some well-known facts about the influence of these axioms of infinity ([28]) to the everyday mathematical practice and point out to some, as of yet not understood, phe-nomena at the level of the third-order arithmetic. Technical details from both set theory and operator algebras are kept at the bare minimum. In the Appendix I include definitions of arithmetical and analytical hierarchies in order to make this paper more accessible to non-logicians. In this paper I am taking a position intermediate between pluralism and non-pluralism (as defined in [34]) with an eye for applications outside of set theory. Acknowledgments This paper is partly based on my talks at the ‘Truth and Infinity ’ work-shop (IMS, 2011) and the ‘Connes Embedding Problem ’ workshop (Ottawa, 2008). I would like to thank the organizers of both meetings. Another driv-ing force for this paper—and much of my work—originated in conversations with functional analysts, too numerous to list here, over the past several
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| 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 it