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1 results

  • Weakly one-based geometric theories

  • Alexander Berenstein, Evgueni Vassiliev
  • Journal:
    The Journal of Symbolic Logic / Volume 77 / Issue 2 / June 2012
    Published online by Cambridge University Press:
    12 March 2014, pp. 392-422
    Print publication:
    June 2012

  • We study the class of weakly locally modular geometric theories introduced in [4], a common generalization of the classes of linear SU-rank 1 and linear o-minimal theories. We find new conditions equivalent to weak local modularity: “weak one-basedness”, absence of type definable “almost quasidesigns”, and “generic linearity”. Among other things, we show that weak one-basedness is closed under reducts. We also show that the lovely pair expansion of a non-trivial weakly one-based ω-categorical geometric theory interprets an infinite vector space over a finite field.