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THEORIES WITH DISTAL SHELAH EXPANSIONS
Part of:
Model theory
Published online by Cambridge University Press: 08 March 2023
Abstract
We show that a complete first-order theory T is distal provided it has a model M such that the theory of the Shelah expansion of M is distal.
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- © The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic
References
REFERENCES
Adler, H., An introduction to theories without the independence property, preprint, 2008.Google Scholar
Aschenbrenner, M., Chernikov, A., Gehret, A., and Ziegler, M., Distality in valued fields and related structures
. Transactions of the American Mathematical Society, vol. 375 (2022), no. 7, pp. 4641–4710.Google Scholar
Chernikov, A. and Simon, P., Externally definable sets and dependent pairs II
. Transactions of the American Mathematical Society, vol. 367 (2015), no. 7, pp. 5217–5235.CrossRefGoogle Scholar
Hrushovski, E., Pillay, A., and Simon, P., Generically stable and smooth measures in NIP theories
. Transactions of the American Mathematical Society, vol. 365 (2013), no. 5, pp. 2341–2366.CrossRefGoogle Scholar
Shelah, S., Classification theory for elementary classes with the dependence property—A modest beginning
. Scientiae Mathematicae Japonicae, vol. 59 (2004), no. 2, pp. 265–316, special issue on set theory and algebraic model theory.Google Scholar
Shelah, S., Dependent first-order theories, continued
. Israel Journal of Mathematics, vol. 173 (2009), 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., A Guide to NIP Theories, Cambridge University Press, Cambridge, 2015, Cambridge Books Online.Google Scholar
Simon, P., Type decomposition in NIP theories
. Journal of the European Mathematical Society (JEMS), vol. 22 (2020), no. 2, pp. 455–476.Google Scholar