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Record W4379010621 · doi:10.1002/malq.202200021

Cofinal types on ω<sub>2</sub>

2023· article· en· W4379010621 on OpenAlexaff
Boriša Kuzeljević, Stevo Todorčević

Bibliographic record

VenueMathematical logic quarterly · 2023
Typearticle
Languageen
FieldMathematics
TopicAdvanced Topology and Set Theory
Canadian institutionsUniversity of Toronto
FundersScience Fund of the Republic of Serbia
KeywordsSuccessor cardinalMathematicsCofinalityClass (philosophy)Simple (philosophy)Type (biology)Discrete mathematicsCountable setUncountable setComputer scienceArtificial intelligenceMathematical analysisEpistemology

Abstract

fetched live from OpenAlex

Abstract In this paper we start the analysis of the class , the class of cofinal types of directed sets of cofinality at most ℵ2. We compare elements of using the notion of Tukey reducibility. We isolate some simple cofinal types in , and then proceed to find some of these types which have an immediate successor in the Tukey ordering of .

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.

How this classification was reachedexpand

Full frame machine prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.003
Version: metacan-v3-hybrid-931329e0061cValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.004
Threshold uncertainty score0.014

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0010.003
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.001
Bibliometrics0.0020.001
Science and technology studies0.0020.003
Scholarly communication0.0030.003
Open science0.0010.001
Research integrity0.0000.001
Insufficient payload (model declined to judge)0.0040.001

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.

Opus teacher head0.047
GPT teacher head0.320
Teacher spread0.273 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it

Classification

machine, unvalidated

Machine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
Study designTheoretical or conceptual
Domainnot available
GenreEmpirical

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".

Quick stats

Citations3
Published2023
Admission routes1
Has abstractyes

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Same venueMathematical logic quarterlySame topicAdvanced Topology and Set TheoryFrench-language works237,207