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2 results

  • Expansions of fields by angular functions

  • Part of
  • David M. Evans
  • Journal:
    Journal of the Institute of Mathematics of Jussieu / Volume 7 / Issue 4 / October 2008
    Published online by Cambridge University Press:
    07 October 2008, pp. 735-750
    Print publication:
    October 2008

  • The notion of an angular function has been introduced by Zilber as one possible way of connecting non-commutative geometry with two ‘counterexamples’ from model theory: the non-classical Zariski curves of Hrushovski and Zilber, and Poizat's field with green points. This article discusses some questions of Zilber relating to existentially closed structures in the class of algebraically closed fields with an angular function.

  • Existentially closed algebras and boolean products

  • Herbert H. J. Riedel
  • Journal:
    The Journal of Symbolic Logic / Volume 53 / Issue 2 / June 1988
    Published online by Cambridge University Press:
    12 March 2014, pp. 571-596
    Print publication:
    June 1988

  • A Boolean product construction is used to give examples of existentially closed algebras in the universal Horn class ISP(K) generated by a universal class K of finitely subdirectly irreducible algebras such that Γa(K) has the Fraser-Horn property. If ⟦a ≠ b⟧ ∩ ⟦c ≠ d ⟧ = ∅ is definable in K and K has a model companion of K-simple algebras, then it is shown that ISP(K) has a model companion. Conversely, a sufficient condition is given for ISP(K) to have no model companion.