Synthese 164 (3):333 - 339 (2008)
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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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.
Three Uses of the Herbrand-Gentzen Theorem in Relating Model Theory and Proof Theory.William Craig - 1957 - Journal of Symbolic Logic 22 (3):269-285.
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.
Citations of this work BETA
Beth Definability, Interpolation and Language Splitting.Rohit Parikh - 2011 - Synthese 179 (2):211 - 221.
Craig Interpolation in the Presence of Unreliable Connectives.João Rasga, Cristina Sernadas & Amlcar Sernadas - 2014 - Logica Universalis 8 (3-4):423-446.
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