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An elementary theory of imbeddability skeleta of discriminator varieties. (Russian) Zbl 0756.08003
Let $$\mathfrak M$$ be a variety of algebras and $$\text{I}\mathfrak M$$ be the set of isomorphic types (isotypes) of algebras from $$\mathfrak M$$. For $$a$$, $$b$$ from $$\mathfrak M$$, there holds $$a\leq b$$ iff there exists an isomorphic embedding of an algebra of isotype $$a$$ in an algebra of isotype $$b$$. The quasi-ordered class $$\langle\text{I}{\mathfrak M},\leq\rangle$$ is called an imbeddability skeleton of $$\mathfrak M$$. The main result of this paper is the following: Theorem. If $$\mathfrak M$$ is a variety containing a quasi-primal algebra without one-element subalgebras, then the elementary theory of the imbeddability skeleton of $$\mathfrak M$$ (i.e. $$\langle\text{I}{\mathfrak M},\leq\rangle$$) is undecidable.

##### MSC:
 08B05 Equational logic, Mal’tsev conditions 03D35 Undecidability and degrees of sets of sentences
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