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The Life and Work of Leon Henkin pp 179–201Cite as

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The Countable Henkin Principle

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Part of the book series: Studies in Universal Logic ((SUL))

Abstract

This is a revised and extended version of an article that encapsulates a key aspect of the “Henkin method” in a general result about the existence of finitely consistent theories satisfying prescribed closure conditions. This principle can be used to give streamlined proofs of completeness for logical systems, in which inductive Henkin-style constructions are replaced by a demonstration that a certain theory “respects” some class of inference rules. The countable version of the principle has a special role and is applied here to omitting-types theorems, and to strong completeness proofs for first-order logic, omega-logic, countable fragments of languages with infinite conjunctions, and a propositional logic with probabilistic modalities. The paper concludes with a topological approach to the countable principle, using the Baire Category Theorem.

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Author information

Authors and Affiliations

  1. School of Mathematics, Statistics and Operations Research, Victoria University of Wellington, PO Box 600, Wellington, 6140, New Zealand

    Robert Goldblatt

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  1. Robert Goldblatt
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Correspondence to Robert Goldblatt .

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Editors and Affiliations

  1. Department of Philosophy, Logic and Aesthetics, University of Salamanca, Salamanca, Spain

    María Manzano

  2. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary

    Ildikó Sain

  3. Department of Logic and Philosophy of Science, Autonomous University of Madrid, Madrid, Spain

    Enrique Alonso

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Goldblatt, R. (2014). The Countable Henkin Principle. In: Manzano, M., Sain, I., Alonso, E. (eds) The Life and Work of Leon Henkin. Studies in Universal Logic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-09719-0_13

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