Reports on Mathematical Logic

No. 36

Tadeusz LITAK:

A continuum of incomplete intermediate logics

A b s t r a c t. Although in 1977 V.B. Shehtman constructed the first Kripke incomplete intermediate logic, no-one in the known literature has completed his work by constructing a continuum of such logics. After a substantial reminder on how an incomplete logic can be obtained, I will construct a sequence of frames similar to those used by Jankov and Fine. None of these frames can be reduced by a p-morphism to another; at the same time, there are no p-morphisms from generated subframes of the Fine frame onto any frame from the considered sequence. All of the frames satisfy all of Shehtman's axioms. Therefore, by using the characteristic formulas of the frames from the sequence it is possible to obtain the desired conclusion.

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