Abstract
Call X eliminable if for every finite set S, if there exists a closed tableau for {S,X} and a closed tableau for {S,X̅}, then there exists a closed tableau for S. It is an immediate corollary of the Completeness theorem for tableaux that every X is eliminable. For suppose there is a closed tableau for {S,X} and a closed tableau for {S,X̅}. Then both {S,X} and {S,X̅} are unsatisfiable, hence S is unsatisfiable (because in any interpretation at least one of X, X̅ is true). Then by the Completeness theorem, there must be a closed tableau for S.
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© 1968 Springer-Verlag Berlin · Heidelberg
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Smullyan, R.M. (1968). Elimination Theorems. 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_12
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DOI: https://doi.org/10.1007/978-3-642-86718-7_12
Publisher Name: Springer, Berlin, Heidelberg
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