Title: Two Undecidability Results using Modified Boolean Powers
Abstract: In this paper we will give brief proofs of two results on the undecidability of a first-order theory using a construction which we call a modified Boolean power. Modified Boolean powers were introduced by Burris in late 1978, and the first results were announced in [ 2 ]. Subsequently we succeeded in using this construction to prove the results in this paper, namely Ershov's theorem that every variety of groups containing a finite non-abelian group has an undecidable theory, and Zamjatin's theorem that a variety of rings with unity which is not generated by finitely many finite fields has an undecidable theory. Later McKenzie further modified the construction mentioned above, and combined it with a variant of one of Zamjatin's constructions to prove the sweeping main result of [ 3 ]. The proofs given here have the advantage (over the original proofs) that they use a single construction.
Publication Year: 1982
Publication Date: 1982-04-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 3
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