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## Equations and equational theories

We define a formula (phi)(x;t)(' )in a first-order language L, to be an equation in a category of L-structures if, for any H in , and set p = {(phi)(x;a(,i));(' )i (ELEM) I, a(,i)(' )(ELEM) H} there is a finite set I(,0) (L-HOOK) I such that for any f:H(--->)F in ,(' )(INTERSECT)(,i(ELEM)I(,0))(phi)(F;fa(,i)) =(' )(INTERSECT)(,i(ELEM)I)(phi)(F;fa(,i)). / We say that a complete theory T is equational if any formula is equivalent in T to a boolean combination of equations in od(T), and we note that equational theories are stable. / Thus, we develop a theory of independence with respect to equations in general categories of structures, which is similar to the one introduced in stability (and actually identical to it in the case of equational theories) but which, in our context, have an algebraic character. / We then compare the concepts introduced in stability theory to corresponding notions in the context of equational theories.

Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.71873 |

Date | January 1984 |

Creators | Srour, Gabriel, 1958- |

Publisher | McGill University |

Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |

Language | English |

Detected Language | English |

Type | Electronic Thesis or Dissertation |

Format | application/pdf |

Coverage | Doctor of Philosophy (Department of Mathematics and Statistics.) |

Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |

Relation | alephsysno: 000220215, proquestno: AAINK66606, Theses scanned by UMI/ProQuest. |

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