The road to two theorems of logic

Synthese 164 (3):333 - 339 (2008)
Abstract
Work on how to axiomatize the subtheories of a first-order theory in which only a proper subset of their extra-logical vocabulary is being used led to a theorem on recursive axiomatizability and to an interpolation theorem for first-order logic. There were some fortuitous events and several logicians played a helpful role.
Keywords Recursive axiomatizability  Interpolation for first-order logic  Robinson’s joint consistency theorem  Beth’s definability theorem  Linear reasoning and the Herbrand–Gentzen theorem
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DOI 10.1007/s11229-008-9353-3
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References found in this work BETA

On Computable Numbers, with an Application to the Entscheidungsproblem.Alan Turing - 1936 - Proceedings of the London Mathematical Society 42 (1):230-265.
On Axiomatizability Within a System.William Craig - 1953 - Journal of Symbolic Logic 18 (1):30-32.
On Padoa's Method in the Theory of Definition.E. W. Beth - 1956 - Journal of Symbolic Logic 21 (2):194-195.
Finite Axiomatizability Using Additional Predicates.W. Craig & R. L. Vaught - 1958 - Journal of Symbolic Logic 23 (3):289-308.

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