Approximate subgroups with bounded VC-dimension

DOI10.1007/s00208-022-02524-3arXiv2004.05666OpenAlexW3015235911MaRDI QIDQ6144265

Anand Pillay, Gabriel Conant

Publication date: 29 January 2024

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.05666

Mathematics Subject Classification ID

Classification theory, stability, and related concepts in model theory (03C45) Ultraproducts and related constructions (03C20) Inverse problems of additive number theory, including sumsets (11P70) Arithmetic combinatorics; higher degree uniformity (11B30)

Cites Work

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• Approximate subgroups
• VC-sets and generic compact domination
• On NIP and invariant measures
• Classification theory and the number of non-isomorphic models.
• Generalized arithmetical progressions and sumsets
• Bounded VC-dimension implies a fractional Helly theorem
• The structure of approximate groups.
• On the Bogolyubov-Ruzsa lemma
• A model-theoretic note on the Freiman-Ruzsa theorem
• Structure and regularity for subsets of groups with finite VC-dimension
• New proofs of Plünnecke-type estimates for product sets in groups
• Product set estimates for non-commutative groups
• A Szemerédi-type regularity lemma in abelian groups, with applications
• Hyperimaginaries and automorphism groups
• Lectures on approximate groups and Hilbert’s 5th problem
• Stable group theory and approximate subgroups
• ON A NONABELIAN BALOG–SZEMERÉDI-TYPE LEMMA
• SETS WITH SMALL SUMSET AND RECTIFICATION
• Convolutions of sets with bounded VC-dimension are uniformly continuous
• Topological dynamics of definable group actions
• Stable arithmetic regularity in the finite field model
• TYPE-DEFINABILITY, COMPACT LIE GROUPS, AND o-MINIMALITY
• On finite sets of small tripling or small alternation in arbitrary groups
• Quantitative structure of stable sets in arbitrary finite groups
• Quantitative structure of stable sets in finite abelian groups
• Pseudofinite groups and VC-dimension
• Efficient arithmetic regularity and removal lemmas for induced bipartite patterns
• A group version of stable regularity
• A Guide to NIP Theories
• Rosenthal compacta and NIP formulas
• Freiman's theorem in an arbitrary abelian group
• Groups, measures, and the NIP
• On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities