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An abstract setting for Henkin proofs

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Abstract

A general result is proved about the existence of maximally consistent theories satisfying prescribed closure conditions. The principle is then used to give ‘streamlined’ proofs of completeness and omitting-types theorems, in which inductive Henkin-style constructions are replaced by a demonstration that a certain theory ‘respects’ a certain class of ‘inference rules’.

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References

  1. Barwise, Jon: 1975, Admissible Sets and Structures, Springer-Verlag, Berlin, Heidelberg.

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  2. Henkin, Leon: 1949, ‘The completeness of the first-order functional calculus’, J. Symbolic Logic 14, 159–166.

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  3. Sacks, Gerald E.: 1972, Saturated Model Theory, W. A. Benjamin, Reading, Massachusetts.

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Authors and Affiliations

  1. Mathematics Dept., Victoria University, Wellington, New Zealand

    Robert Goldblatt

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  1. Robert Goldblatt
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Goldblatt, R. An abstract setting for Henkin proofs. Topoi 3, 37–41 (1984). https://doi.org/10.1007/BF00136118

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  • DOI: https://doi.org/10.1007/BF00136118

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