Abstract
Let h − the Hilbert system in a propositional language with ∧, ∨, →, obtained from h by Definition 4.1.1 by dropping axiom (g). So h − is the negationless fragment of h. The deduction theorem holds for h −, the proof being as in 2.1.13 and h − is complete for the class of propositional Kripke structures of Definition 4.1.8 with [A] t defined as in 4.1.8 for any wff A. The completeness proof is the same as the one given in Section 1 of Chapter 4.
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© 1981 Springer Science+Business Media Dordrecht
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Gabbay, D.M. (1981). Propositional Connectives. In: Semantical Investigations in Heyting’s Intuitionistic Logic. Synthese Library, vol 148. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2977-2_8
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DOI: https://doi.org/10.1007/978-94-017-2977-2_8
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-8362-3
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