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Interpretability logic
- Mathematical Logic, Proceedings of the 1988 Heyting Conference
, 1990
"... Interpretations are much used in metamathematics. The first application that comes to mind is their use in reductive Hilbert-style programs. Think of the kind of program proposed by Simpson, Feferman or Nelson (see Simpson[1988], Feferman[1988], Nelson[1986]). Here they serve to compare the strength ..."
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Cited by 27 (9 self)
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Interpretations are much used in metamathematics. The first application that comes to mind is their use in reductive Hilbert-style programs. Think of the kind of program proposed by Simpson, Feferman or Nelson (see Simpson[1988], Feferman[1988], Nelson[1986]). Here they serve to compare the strength of theories, or better to prove
No Escape from Vardanyan’s Theorem
, 2003
"... Vardanyan’s Theorem states that the set of PA-valid principles of Quantified Modal Logic, QML, is complete Π 0 2. We generalize this result to a wide class of theories. The crucial step in the generalization is avoiding the use of Tennenbaum’s Theorem. ..."
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Cited by 1 (0 self)
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Vardanyan’s Theorem states that the set of PA-valid principles of Quantified Modal Logic, QML, is complete Π 0 2. We generalize this result to a wide class of theories. The crucial step in the generalization is avoiding the use of Tennenbaum’s Theorem.
