MétaCan
Menu
Back to cohort
Record W4412647423 · doi:10.55016/ojs/cdm.v2i2.61935

Martin's axiom and almost disjoint families

2007· article· en· W4412647423 on OpenAlexvenueno aff
Latifa Faouzi

Bibliographic record

VenueContributions to Discrete Mathematics · 2007
Typearticle
Languageen
FieldMathematics
TopicAdvanced Topology and Set Theory
Canadian institutionsnot available
Fundersnot available
KeywordsDisjoint setsMathematicsAxiom of choiceCombinatoricsZermelo–Fraenkel set theoryAxiomUrelementDiscrete mathematicsGenealogySet (abstract data type)Set theoryComputer science

Abstract

fetched live from OpenAlex

Assuming \rfsMA+ℵ1<2ℵ0, we show that, for any κ,λ<2ℵ0 and any almost disjoint family \setnaii<λ of countable subsets of κ, with λ<2ℵ0, there is a partition \setnpnn∈ω of κ so that pn∩ai is finite for each (i,n)∈λ×ω.

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)0.003
metaresearch head score (Gemma)0.005
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: none
Teacher disagreement score0.007
Threshold uncertainty score0.025

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0030.005
Meta-epidemiology (narrow)0.0010.001
Meta-epidemiology (broad)0.0010.002
Bibliometrics0.0010.001
Science and technology studies0.0030.005
Scholarly communication0.0020.007
Open science0.0010.005
Research integrity0.0010.003
Insufficient payload (model declined to judge)0.0070.001

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 head0.017
GPT teacher head0.346
Teacher spread0.329 · 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

Citations0
Published2007
Admission routes1
Has abstractyes

Explore more

Same venueContributions to Discrete MathematicsSame topicAdvanced Topology and Set TheoryFrench-language works237,207