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Trois couleurs: A new non-equational theory

Volume 254 / 2021

Amador Martin-Pizarro, Martin Ziegler Fundamenta Mathematicae 254 (2021), 313-333 MSC: Primary 03C45. DOI: 10.4064/fm953-9-2020 Published online: 11 February 2021

Abstract

A first order theory is equational if every definable set is a Boolean combination of instances of equations, that is, of formulae such that the family of finite intersections of instances has the descending chain condition. Equationality is a strengthening of stability yet so far only two examples of non-equational stable theories are known. We construct non-equational $\omega $-stable theories by a suitable colouring of the free pseudospace, based on Hrushovski and Srour’s original example.

Authors

  • Amador Martin-PizarroMathematisches Institut
    Albert-Ludwigs-Universität Freiburg
    Ernst-Zermelo-Str. 1
    D-79104 Freiburg, Germany
    e-mail
  • Martin ZieglerMathematisches Institut
    Albert-Ludwigs-Universität Freiburg
    Ernst-Zermelo-Str. 1
    D-79104 Freiburg, Germany
    e-mail

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