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Record W2964076955 · doi:10.1142/s0219061310000936

A DICHOTOMY FOR THE NUMBER OF ULTRAPOWERS

2010· article· en· W2964076955 on OpenAlex

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.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueJournal of Mathematical Logic · 2010
Typearticle
Languageen
FieldMathematics
TopicAdvanced Operator Algebra Research
Canadian institutionsYork University
Fundersnot available
KeywordsCardinal number (linguistics)Cardinality (data modeling)MathematicsMetric (unit)Property (philosophy)CombinatoricsDiscrete mathematicsComputer scienceEpistemologyPhilosophyLinguistics

Abstract

fetched live from OpenAlex

We prove a strong dichotomy for the number of ultrapowers of a given model of cardinality ≤ 2 ℵ 0 associated with nonprincipal ultrafilters on ℕ. They are either all isomorphic, or else there are 2 2 ℵ 0 many nonisomorphic ultrapowers. We prove the analogous result for metric structures, including C*-algebras and II 1 factors, as well as their relative commutants and include several applications. We also show that the CAF001-algebra [Formula: see text] always has nonisomorphic relative commutants in its ultrapowers associated with nonprincipal ultrafilters on ℕ.

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 imitation

Not 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.

metaresearch head score (Codex)0.002
metaresearch head score (Gemma)0.007
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesInsufficient payload (model declined to judge)
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 score0.062
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0020.007
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0010.000
Research integrity0.0000.001
Insufficient payload (model declined to judge)0.0010.000

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.

Opus teacher head0.064
GPT teacher head0.421
Teacher spread0.357 · 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