Definability theorems in normal extensions of the probability logic

Studia Logica 48 (4):495-507 (1989)


Three variants of Beth's definability theorem are considered. Let L be any normal extension of the provability logic G. It is proved that the first variant B1 holds in L iff L possesses Craig's interpolation property. If L is consistent, then the statement B2 holds in L iff L = G + {0}. Finally, the variant B3 holds in any normal extension of G

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References found in this work

Pretabular Varieties of Modal Algebras.W. J. Blok - 1980 - Studia Logica 39 (2-3):101 - 124.
[Omnibus Review].William Craig - 1957 - Journal of Symbolic Logic 22 (4):360-363.

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