MétaCan
Menu
Back to cohort
Record W4414266164 · doi:10.64191/zr24040410109

A survey on big Ramsey structures

2025· book-chapter· en· W4414266164 on OpenAlexfundno aff
Jan Hubička, Andy Zucker

Bibliographic record

Venuenot available
Typebook-chapter
Languageen
FieldMathematics
TopicAdvanced Topology and Set Theory
Canadian institutionsnot available
FundersNatural Sciences and Engineering Research Council of CanadaGrantová Agentura České Republiky
KeywordsBig dataRamsey theoryUnary operationSubstructureField (mathematics)

Abstract

fetched live from OpenAlex

In recent years, there has been much progress in the field of structural Ramsey theory, in particular in the study of big Ramsey degrees. In all known examples of infinite structures with finite big Ramsey degrees, there is in fact a single expansion of the structure, called a big Ramsey structure, which correctly encodes the exact big Ramsey degrees of every finite substructure simultaneously. The first half of the article collects facts about this phenomenon that have appeared in the literature into a single cohesive framework, thus offering a conceptual survey of big Ramsey structures. We present some original results indicating that the standard methods of proving finite big Ramsey degrees automatically yield big Ramsey structures, often with desirable extra properties. The second half of the article is a survey in the more traditional sense, discussing numerous examples from the literature and showing how they fit into our framework. We also present some general results on how big Ramsey degrees are affected by expanding structures with unary functions.

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)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow), Insufficient 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: Other · Consensus signal: Other
Teacher disagreement score0.025
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
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 science0.0000.000
Research integrity0.0010.001
Insufficient payload (model declined to judge)0.0030.000

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 head0.073
GPT teacher head0.332
Teacher spread0.258 · 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.

Study designTheoretical or conceptual
Domainnot available
GenreOther

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

Citations1
Published2025
Admission routes1
Has abstractyes

Explore more

Same topicAdvanced Topology and Set TheoryFrench-language works237,207