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THE DEFINABLE (P, Q)-THEOREM FOR DISTAL THEORIES

Published online by Cambridge University Press:  09 November 2017

GARETH BOXALL  and
CHARLOTTE KESTNER
GARETH BOXALL
Affiliation:
DEPARTMENT OF MATHEMATICAL SCIENCES STELLENBOSCH UNIVERSITY STELLENBOSCH 7600, SOUTH AFRICAE-mail: gboxall@sun.ac.za
CHARLOTTE KESTNER
Affiliation:
DEPARTMENT OF PHYSICAL SCIENCES AND COMPUTING JEREMIAH HORROCKS INSTITUTE FOR MATHEMATICS, PHYSICS AND ASTRONOMY UNIVERSITY OF CENTRAL LANCASHIRE FYLDE RD, PRESTON PR1 2HE, UKE-mail: ckestner@uclan.ac.uk
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Abstract

Answering a special case of a question of Chernikov and Simon, we show that any non-dividing formula over a model M in a distal NIP theory is a member of a consistent definable family, definable over M.

Keywords

03C45definable (p,q)distalityforkingNIP
Type
Articles
Information
The Journal of Symbolic Logic , Volume 83 , Issue 1 , March 2018 , pp. 123 - 127
Copyright
Copyright © The Association for Symbolic Logic 2017 

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References

REFERENCES

Chernikov, A. and Kaplan, I., Forking and dividing in NTP2 theories, this Journal, vol. 77 (2012), no. 1, pp. 1–20.Google Scholar
Chernikov, A. and Simon, P., Externally definable sets and dependent pairs II. Transactions of the American Mathematical Society, vol. 367 (2015), pp. 5217–5235.Google Scholar
Shelah, S., Dependent first order theories, continued. Israel Journal of Mathematics, vol. 173 (2009), no. 1, pp. 1–60.Google Scholar
Simon, P., Distal and non-distal NIP theories. Annals of Pure and Applied Logic, vol. 164 (2013), no. 3, pp. 294–318.Google Scholar
Simon, P., Dp-minimality: Invariant types and dp-rank, this Journal, vol. 79 (2014), pp. 1025–1045.Google Scholar
Simon, P., A Guide to NIP Theories, Cambridge University Press, Cambridge, 2015.Google Scholar
Simon, P., Invariant types in NIP theories. Journal of Mathematical Logic, vol. 15 (2015), no. 2, 26 pp.Google Scholar
Simon, P. and Starchenko, S., On forking and definability of types in some dp-minimal theories, this Journal, vol. 79 (2014), pp. 1020–1024.Google Scholar