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Record W1975072530 · doi:10.1017/jsl.2013.6

THE NON-AXIOMATIZABILITY OF O-MINIMALITY

2014· preprint· en· W1975072530 on OpenAlexaff
Alex Rennet

Bibliographic record

VenueJournal of Symbolic Logic · 2014
Typepreprint
Languageen
FieldMathematics
TopicAdvanced Topology and Set Theory
Canadian institutionsUniversity of Toronto
Fundersnot available
KeywordsUltraproductPredicate (mathematical logic)MathematicsDiscrete mathematicsField (mathematics)LambdaFunction (biology)Pure mathematicsComputer scienceProgramming languagePhysics

Abstract

fetched live from OpenAlex

Abstract Fix a language extending the language of ordered fields by at least one new predicate or function symbol. Call an L -structure R pseudo-o-minimal if it is (elementarily equivalent to) an ultraproduct of o-minimal structures. We show that for any recursive list of L -sentences , there is a real closed field satisfying which is not pseudo-o-minimal. This shows that the theory T o−min consisting of those -sentences true in all o-minimal -structures, also called the theory of o-minimality (for L) , is not recursively axiomatizable. And, in particular, there are locally o-minimal, definably complete expansions of real closed fields which are not pseudo-o-minimal.

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 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)0.005
metaresearch head score (Gemma)0.003
Version: codex-gemma-dda1882f352aValidation 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 score0.038
Threshold uncertainty score0.597

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0050.003
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.001
Bibliometrics0.0000.000
Science and technology studies0.0000.001
Scholarly communication0.0000.000
Open science0.0010.000
Research integrity0.0000.001
Insufficient payload (model declined to judge)0.0000.000

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 head0.048
GPT teacher head0.366
Teacher spread0.318 · 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 teacher head, 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
Published2014
Admission routes1
Has abstractyes

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