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Reports on Mathematical Logic

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No. 30

Jerzy HANUSEK

DECIDABILITY OF CLASSES OF FINITE ALGEBRAS WITH A DISTINGUISHED
SUBSET CLOSED UNDER A DISCRIMINATOR CLONE
A b s t r a c t.
We show
that if T is the smallest discriminator clone on a set A, then
the first order theory of finite powers
of a finite algebra ** A** with a distinguished subset
closed under T is decidable. If ** A** is a
primal algebra and C is any discriminator clone on A,
then the first order theory of finite algebras from
* V*(A)
with a distinguished subset closed under C is decidable.
In particular, the first order theory of algebras
from
* V*(A)
with a distinguished subalgebra is decidable.

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