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Reports on Mathematical Logic

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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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