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Record W2022730753 · doi:10.1090/s0002-9939-08-08918-1

On a fragment of the universal Baire property for Σ¹₂ sets

2008· article· en· W2022730753 on OpenAlexaff
Stuart Zoble

Bibliographic record

VenueProceedings of the American Mathematical Society · 2008
Typearticle
Languageen
FieldMathematics
TopicAdvanced Topology and Set Theory
Canadian institutionsUniversity of Toronto
Fundersnot available
KeywordsMathematicsBaire measureOmegaSigmaBaire spaceBaire category theoremEquivalence (formal languages)Pure mathematicsCombinatoricsDiscrete mathematicsPhysics

Abstract

fetched live from OpenAlex

There is a well-known global equivalence between Σ 2 1 \Sigma ^1_2 sets having the universal Baire property, two-step Σ 3 1 \Sigma ^1_3 generic absoluteness, and the closure of the universe under the sharp operation. In this note, we determine the exact consistency strength of Σ 2 1 \Sigma ^1_2 sets being ( 2 ω ) + (2^{\omega })^{+} -cc-universally Baire, which is below 0 # 0^{\#} . In a model obtained, there is a Σ 2 1 \Sigma ^1_2 set which is weakly ω 2 \omega _2 -universally Baire but not ω 2 \omega _2 -universally Baire.

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)0.002
metaresearch head score (Gemma)0.006
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 score0.020
Threshold uncertainty score0.066

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0020.006
Meta-epidemiology (narrow)0.0010.001
Meta-epidemiology (broad)0.0010.003
Bibliometrics0.0020.002
Science and technology studies0.0030.005
Scholarly communication0.0040.015
Open science0.0010.005
Research integrity0.0010.004
Insufficient payload (model declined to judge)0.0200.004

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 head0.027
GPT teacher head0.284
Teacher spread0.257 · 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
Published2008
Admission routes1
Has abstractyes

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Same venueProceedings of the American Mathematical SocietySame topicAdvanced Topology and Set TheoryFrench-language works237,207