Recursive Equivalence

Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE2, volume 81)


Let L be a complete effectively presented countable first order language with identity. Let L(C) be the extension of L obtained by adding a fully effective countably infinite set of individual constants. If T′ is a complete theory in L(C) and T a theory in L then T′ is said to be a witness completion of T if T′ ⊇ T and whenever ∃ υ n φ (υ n ) is in T, then φ (c) is in T′ for some cC. The Henkin-Hasenjaeger proof of completeness of first order logic has an obvious effective version obtained by simply making all listings effective (see Mendelson [1964] exercise p. 65 and Proposition 2.12). There is also an obvious relativized version.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1974

Authors and Affiliations

  1. 1.Monash UniversityMelbourneAustralia
  2. 2.Cornell UniversityIthacaUSA

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