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Completeness of the functional calculus of first order

Worked out under the direction of Prof. Dr. J. Słupecki summary

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References

  1. We are modifying slightly the original formulation of Skolem-Löwenheim's theorem.

  2. We are keeping in this summary the numeration given to definitions, lemmas and theorems in the full texst.

  3. The definition of satisfying is given on p. 217 (1d), 2d), (3d) and (4d).

  4. Let us note, that the proof of this theorem remains valid when the rules of inference are so modified that the following reverse theorem remains also valid:if all the formulae belonging to U are simultaneously satisfiable, then Uis consistent.

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  1. J. Reichbach
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I have read this paper at a meeting of Prof. Słupecki's seminar. I have also presented its results at a meeting of Wrocław Section of Polish Mathematical Society on December 5-th 1952. The proof of theorems 1 and 2 contained in this paper has been worked out after the publication of L. Henkin's study [4] and independently of later published discussions on this subject. This proof is, like that of Henkin, elementary.

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Reichbach, J. Completeness of the functional calculus of first order. Stud Logica 2, 245–250 (1955). https://doi.org/10.1007/BF02124776

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  • DOI: https://doi.org/10.1007/BF02124776

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