An Institution-Independent Proof of the Robinson Consistency Theorem

Abstract

We prove an institutional version of A. Robinson’s Consistency Theorem. This result is then appliedto the institution of many-sorted first-order predicate logic and to two of its variations, infinitary and partial, obtaining very general syntactic criteria sufficient for a signature square in order to satisfy the Robinson consistency and Craig interpolation properties.

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Correspondence to Daniel Gâinâ.

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Presented by Robert Goldblatt

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Gâinâ, D., Popescu, A. An Institution-Independent Proof of the Robinson Consistency Theorem. Stud Logica 85, 41–73 (2007). https://doi.org/10.1007/s11225-007-9022-4

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Keywords

  • institution
  • Robinson consistency
  • Craig interpolation
  • elementary diagram
  • many-sorted first-order logic