Ramsey growth in some NIP structures

Kurzanzeige
dc.contributor.authorChernikov, Artem
dc.contributor.authorStarchenko, Sergei
dc.contributor.authorThomas, Margaret E. M.
dc.date.accessioned2021-04-29T11:47:34Z
dc.date.available2021-04-29T11:47:34Z
dc.date.issued2021eng
dc.description.abstractWe investigate bounds in Ramsey’s theorem for relations definable in NIP structures. Applying model-theoretic methods to finitary combinatorics, we generalize a theorem of Bukh and Matousek (Duke Mathematical Journal 163(12) (2014), 2243–2270) from the semialgebraic case to arbitrary polynomially bounded o -minimal expansions of R , and show that it does not hold in Rexp . This provides a new combinatorial characterization of polynomial boundedness for o -minimal structures. We also prove an analog for relations definable in P -minimal structures, in particular for the field of the p -adics. Generalizing Conlon et al. (Transactions of the American Mathematical Society 366(9) (2014), 5043–5065), we show that in distal structures the upper bound for k -ary definable relations is given by the exponential tower of height k−1 .eng
dc.description.versionpublishedde
dc.identifier.arxiv1609.05951v3eng
dc.identifier.doi10.1017/S1474748019000100eng
dc.identifier.ppn1757277587
dc.identifier.urihttps://kops.uni-konstanz.de/handle/123456789/53535
dc.language.isoengeng
dc.rightsterms-of-use
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dc.subjecto-minimality; NIP; Ramsey's theorem; p-minimality; polynomially boundedeng
dc.subject.ddc510eng
dc.titleRamsey growth in some NIP structureseng
dc.typeJOURNAL_ARTICLEde
dspace.entity.typePublication
kops.citation.bibtex
@article{Chernikov2021Ramse-53535,
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  doi={10.1017/S1474748019000100},
  title={Ramsey growth in some NIP structures},
  number={1},
  volume={20},
  issn={1474-7480},
  journal={Journal of the Institute of Mathematics of Jussieu},
  pages={1--29},
  author={Chernikov, Artem and Starchenko, Sergei and Thomas, Margaret E. M.}
}
kops.citation.iso690CHERNIKOV, Artem, Sergei STARCHENKO, Margaret E. M. THOMAS, 2021. Ramsey growth in some NIP structures. In: Journal of the Institute of Mathematics of Jussieu. Cambridge University Press. 2021, 20(1), pp. 1-29. ISSN 1474-7480. eISSN 1475-3030. Available under: doi: 10.1017/S1474748019000100deu
kops.citation.iso690CHERNIKOV, Artem, Sergei STARCHENKO, Margaret E. M. THOMAS, 2021. Ramsey growth in some NIP structures. In: Journal of the Institute of Mathematics of Jussieu. Cambridge University Press. 2021, 20(1), pp. 1-29. ISSN 1474-7480. eISSN 1475-3030. Available under: doi: 10.1017/S1474748019000100eng
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