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Publisher: Cambridge University Press
Languages: English
Types: Article
Subjects: G110
We clarify and correct some statements and results in the literature concerning unimodularity in the sense of Hrushovski [7], and measur- ability in the sense of Macpherson and Steinhorn [8], pointing out in particular that the two notions coincide for strongly minimal struc- tures and that another property from [7] is strictly weaker, as well as “completing” Elwes’ proof [5] that measurability implies 1-basedness for stable theories.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • [1] S. Buechler, Locally modular theories of finite rank, Annals of Pure and Applied Logic, 30 (1986), 83-95.
    • [2] S. Buechler, On nontrivial types of U -rank 1, Journal of Symbolic Logic, 52 (1987), 548-541.
    • [3] S. Buechler, The geometry of weakly minimal types, Journal of Symbolic Logic, 50 (1985), 1044-1053.
    • [4] Z. Chatzidakis, L. van den Dries, and A. Macintyre, Definable sets over finite fields. J. Reine Angew. Math 427 (1992), 107-135.
    • [5] R. Elwes, Asymptotic classes of finite structures, Journal of Symbolic Logic, 72 (2007), 418-438.
    • [6] R. Elwes and D. Macpherson, A survey of asymptotic classes and measurable structures, in Model Theory with Applications to Algebra and Analysis, vol. 2, (edited by Chatzidakis, Macpherson, Pillay, Wilkie), LMS Lecture Notes Series 350, Cambridge University Press, 2008.
    • [7] E. Hrushovski, Unimodular minimal structures, Journal of the London Math. Society, 46 (1992), 385-396.
    • [8] D. Macpherson and C. Steinhorn, One-dimensional asymptotic classes of finite structures, Transactions AMS, 360 (2008), 411-448.
    • [9] A. Pillay, Geometric Stability Theory, Oxford University Press, 1996.
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