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An extended Herbrand theorem for first-order theories with equality interpreted in partial algebras

  • Uwe Petermann
Communications
Part of the Lecture Notes in Computer Science book series (LNCS, volume 379)

Abstract

Two derivation operations are defined which are sound and complete for interpretations of first-order theories with equality in classes of partial algebraic structures. Łoś' theorem on ultraproducts has been generalized for such interpretations.

The following generalized form of Herbrand's theorem is proved: For an arbitrary first-order theory & and an arbitrary formula α may be constructed an enumerable set of open formulas Hα such that & ↣ α holds iff there exists β ε Hα with & ↣ β. whereby ↣ denotes either the usual or one of the mentioned above derivation operators. The enumeration of Hα is determined by a procedure which is closely related to the connection method proof procedure.

Key words

Theorem Proving Herbrand Disjunctions Connection Method Partial Algebras Built in Theories 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Uwe Petermann
    • 1
  1. 1.Department of MathematicsKarl Marx University Karl-Marx-PlatzLeipzigGDR

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