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Record W2072020033 · doi:10.2307/2695059

Definability in low simple theories

2000· article· en· W2072020033 on OpenAlexaff
Ziv Shami

Bibliographic record

VenueJournal of Symbolic Logic · 2000
Typearticle
Languageen
FieldMathematics
TopicAdvanced Topology and Set Theory
Canadian institutionsMcMaster University
Fundersnot available
KeywordsSimple (philosophy)MathematicsBounded functionContext (archaeology)Model theoryEquivalence relationClass (philosophy)Equivalence (formal languages)Pure mathematicsDiscrete mathematicsCombinatoricsComputer scienceMathematical analysisEpistemology

Abstract

fetched live from OpenAlex

In 1978 Shelah introduced a new class of theories, called simple (see [Shi]) which properly contained the class of stable theories. Shelah generalized part of the theory of forking to the simple context. After approximately 15 years of neglecting the general theory (although there were works by Hrushovski on finite rank with a definability assumption, as well as deep results on specific simple theories by Cherlin, Hrushovski, Chazidakis, Macintyre and Van den dries, see [CH], [CMV], [HP1], [HP2], [ChH]) there was a breakthrough, initiated with the work of Kim ([K1]). Kim proved that almost all the technical machinery of forking developed in the stable context could be generalized to simple case. However, the theory of multiplicity (i.e., the description of the (bounded) set of non forking extensions of a given complete type) no longer holds in the context of simple theories. Indeed, by contrast to simple theories, stable theories share a strong amalgamation property of types, namely if p and q are two “free” complete extensions over a superset of A , and there is no finite equivalence relation over A which separates them, then the conjunction of p and q is consistent (and even free over A .) In [KP] Kim and Pillay proved a weak version of this property for any simple theory, namely “the Independence Theorem for Lascar strong types”. This was a weaker version both because of the requirement that the sets of parameters of the types be mutually independent, as well as the use of Lascar strong types instead of the usual strong types. A very fundamental and interesting problem is whether the independence theorem can be proved for any simple theory, using only the usual strong types. In 1997 Buechler proved ([Bu]) the strong-type version of the independence theorem for an important subclass of simple theories, namely the class of low theories (which includes the class of stable theories and the class of supersimple theories of finite D-rank.)

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)0.004
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 score0.005
Threshold uncertainty score0.022

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0020.004
Meta-epidemiology (narrow)0.0000.001
Meta-epidemiology (broad)0.0010.001
Bibliometrics0.0020.001
Science and technology studies0.0020.006
Scholarly communication0.0030.006
Open science0.0010.003
Research integrity0.0010.004
Insufficient payload (model declined to judge)0.0050.001

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 head0.023
GPT teacher head0.323
Teacher spread0.300 · 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

Citations18
Published2000
Admission routes1
Has abstractyes

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