The road to two theorems of logic

Synthese 164 (3):333 - 339 (2008)
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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.

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References found in this work

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.
Finite axiomatizability using additional predicates.W. Craig & R. L. Vaught - 1958 - Journal of Symbolic Logic 23 (3):289-308.
Linear reasoning. A new form of the herbrand-Gentzen theorem.William Craig - 1957 - Journal of Symbolic Logic 22 (3):250-268.

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