Pith. sign in

REVIEW 1 cited by

Definable groups for dependent and 2-dependent theories

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv math/0703045 v5 pith:NL2PAFSM submitted 2007-03-01 math.LO

Saharon Shelah This is my paper
classification math.LO
keywords dependentdefinabletheoriesboundedfirstindexkappaorder
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

Let $T$ be a (first order complete) dependent theory, ${\mathfrak{C}}$ a $\bar\kappa$-saturated model of $T$ and $G$ a definable subgroup which is abelian. Among subgroups of bounded index which are the union of $<\bar\kappa$ type definable subsets there is a minimal one, i.e. their intersection has bounded index. In fact, the bound is $\leq 2^{|T|}$. We then deal with 2-dependent theories, a wider class of first order theories.

Discussion (0). Sign in to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Taking model-complete cores

    math.LO 2025-12 conditional novelty 8.0 of 10

    Core companions preserve stability, NIP, simplicity, and NSOP_k, but the classes of structures interpretable over (N;=) and (Q;<) are not closed under taking core companions.

Pith tools