Abstract
A formula Z is called an interpolation formula for a formula X ⊃ Y if all predicates and parameters of Z occur in both X and in Y, and if X ⊃ Z, Z ⊃ y are both valid. Craig’s celebrated Interpolation lemma says that for any valid sentence X ⊃ Y: (i) if X, Y have at least one predicate in common, then there exists an interpolation sentence for X ⊃ Y; (ii) if X, Y have no predicates in common, then either Y is valid or X is unsatisfiable.
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© 1968 Springer-Verlag Berlin · Heidelberg
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Smullyan, R.M. (1968). Craig’s Interpolation Lemma and Beth’s Definability Theorem. In: First-Order Logic. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 43. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-86718-7_15
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DOI: https://doi.org/10.1007/978-3-642-86718-7_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-86720-0
Online ISBN: 978-3-642-86718-7
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