Bimodal logics for extensions of arithmetical theories
Keyword(s):
AbstractWe characterize the bimodal provability logics for certain natural (classes of) pairs of recursively enumerable theories, mostly related to fragments of arithmetic. For example, we shall give axiomatizations, decision procedures, and introduce natural Kripke semantics for the provability logics of (IΔ0 + EXP, PRA); (PRA, IΣn); (IΣm, IΣn) for 1 ≤ m < n; (PA, ACA0); (ZFC, ZFC + CH); (ZFC, ZFC + ¬CH) etc. For the case of finitely axiomatized extensions of theories these results are extended to modal logics with propositional constants.
2019 ◽
Vol 30
(2)
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pp. 549-560
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2020 ◽
Vol 30
(7)
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pp. 1305-1329
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2000 ◽
Vol 162
(1-2)
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pp. 158-178
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2015 ◽
Vol 28
(5)
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pp. 967-989
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Keyword(s):
2019 ◽
Vol 56
(4)
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pp. 454-481