Abstract
Let T be a set of axioms. This set gives rise to a theory T H in Heyting’s predicate logic and a theory T C in the classical predicate logic. More generally, if X is any intermediate logic, we get a theory T X.
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Notes
Section 6 on the undecidability of 2nd order intuitionistic propositional calculus is based on the paper by the author in the Archiv für Math. Logic 1974. Sobolev 1977 pointed out that the original definition of N(x) (Definition 2a in my paper of 1974) allows for the case x = f. Thus in the definition of N(x) in this book (Section 6) the conjunct (1x→E) is added and the case x = f is excluded. Sobolev 1977 suggests another way of correcting the gap. He changes the definition of D(x) to handle the case x = f.
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© 1981 Springer Science+Business Media Dordrecht
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Gabbay, D.M. (1981). Undecidability Results. In: Semantical Investigations in Heyting’s Intuitionistic Logic. Synthese Library, vol 148. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2977-2_15
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DOI: https://doi.org/10.1007/978-94-017-2977-2_15
Publisher Name: Springer, Dordrecht
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